Calculo numerico 1991

53
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Transcript of Calculo numerico 1991

Page 1: Calculo numerico   1991

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middot9 ~~ ~ ~rNlfW1 n

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b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

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11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

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3gtlamp8t ~4

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t 6-~1 Rt eurot-1o)

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--

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o~-~

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----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

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===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

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11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

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t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

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S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

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2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

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~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

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n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

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~Q o ~~~

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Qhtamp NKAgrave ~) INQ

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i fj a~i

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G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

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j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

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01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

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ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

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l1tQ+c ) d 4-1- + ~

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( ~~l~

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joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

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( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

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ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

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ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

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2 O lOacutes

6000

f lt1--)

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o

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~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

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bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

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a ltl = O a l-z) -04

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bull t bull

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lr~rfSsi dade

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f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 2: Calculo numerico   1991

T I

~

~~-------~

30 3 4 b

~o

1- -~

0

---~---------- -- ~~~- -------~

Clti~Qu)o J~00middot

bl~ ~i~ (~~ de ) ~~ ) 4 e

OC=- bull b I Q~

ltamp- ~ c1 )81 ~~ ~~ ~~ ~ltI

a~~ ~ ~ 0I ~J d2 Cbull J~~ t l ~ ft~) J)euroTS~

o Xi

i ~ ~ Jgt~ c~~~J~~ CNbamp ~bull ~ lt~ccedil ~ ~ (() 3gtG$e ~I~~)= sd 9- 0 J1l ~e~1Ndo ~ 3 ~1 ~~) j)Ase ~)t(3)~middoth ~3 73

middot9 ~~ ~ ~rNlfW1 n

O

~~ 1J ~ 51~ ~NQo (5) o9~llliYK1l

-1( e

~~ 1J ~ eacute 55

QiNQo C5) ~IC((K)~

-1t e

bull I a li o

fWvfIIIacute)iC-Q ~~~ YQo l~

~ A~~~ e ~~

- _~_ --shy~

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 3: Calculo numerico   1991

~~-------~

30 3 4 b

~o

1- -~

0

---~---------- -- ~~~- -------~

Clti~Qu)o J~00middot

bl~ ~i~ (~~ de ) ~~ ) 4 e

OC=- bull b I Q~

ltamp- ~ c1 )81 ~~ ~~ ~~ ~ltI

a~~ ~ ~ 0I ~J d2 Cbull J~~ t l ~ ft~) J)euroTS~

o Xi

i ~ ~ Jgt~ c~~~J~~ CNbamp ~bull ~ lt~ccedil ~ ~ (() 3gtG$e ~I~~)= sd 9- 0 J1l ~e~1Ndo ~ 3 ~1 ~~) j)Ase ~)t(3)~middoth ~3 73

middot9 ~~ ~ ~rNlfW1 n

O

~~ 1J ~ 51~ ~NQo (5) o9~llliYK1l

-1( e

~~ 1J ~ eacute 55

QiNQo C5) ~IC((K)~

-1t e

bull I a li o

fWvfIIIacute)iC-Q ~~~ YQo l~

~ A~~~ e ~~

- _~_ --shy~

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 4: Calculo numerico   1991

30 3 4 b

~o

1- -~

0

---~---------- -- ~~~- -------~

Clti~Qu)o J~00middot

bl~ ~i~ (~~ de ) ~~ ) 4 e

OC=- bull b I Q~

ltamp- ~ c1 )81 ~~ ~~ ~~ ~ltI

a~~ ~ ~ 0I ~J d2 Cbull J~~ t l ~ ft~) J)euroTS~

o Xi

i ~ ~ Jgt~ c~~~J~~ CNbamp ~bull ~ lt~ccedil ~ ~ (() 3gtG$e ~I~~)= sd 9- 0 J1l ~e~1Ndo ~ 3 ~1 ~~) j)Ase ~)t(3)~middoth ~3 73

middot9 ~~ ~ ~rNlfW1 n

O

~~ 1J ~ 51~ ~NQo (5) o9~llliYK1l

-1( e

~~ 1J ~ eacute 55

QiNQo C5) ~IC((K)~

-1t e

bull I a li o

fWvfIIIacute)iC-Q ~~~ YQo l~

~ A~~~ e ~~

- _~_ --shy~

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 5: Calculo numerico   1991

Clti~Qu)o J~00middot

bl~ ~i~ (~~ de ) ~~ ) 4 e

OC=- bull b I Q~

ltamp- ~ c1 )81 ~~ ~~ ~~ ~ltI

a~~ ~ ~ 0I ~J d2 Cbull J~~ t l ~ ft~) J)euroTS~

o Xi

i ~ ~ Jgt~ c~~~J~~ CNbamp ~bull ~ lt~ccedil ~ ~ (() 3gtG$e ~I~~)= sd 9- 0 J1l ~e~1Ndo ~ 3 ~1 ~~) j)Ase ~)t(3)~middoth ~3 73

middot9 ~~ ~ ~rNlfW1 n

O

~~ 1J ~ 51~ ~NQo (5) o9~llliYK1l

-1( e

~~ 1J ~ eacute 55

QiNQo C5) ~IC((K)~

-1t e

bull I a li o

fWvfIIIacute)iC-Q ~~~ YQo l~

~ A~~~ e ~~

- _~_ --shy~

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 6: Calculo numerico   1991

~~ 1J ~ 51~ ~NQo (5) o9~llliYK1l

-1( e

~~ 1J ~ eacute 55

QiNQo C5) ~IC((K)~

-1t e

bull I a li o

fWvfIIIacute)iC-Q ~~~ YQo l~

~ A~~~ e ~~

- _~_ --shy~

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 7: Calculo numerico   1991

~~ 1J ~ eacute 55

QiNQo C5) ~IC((K)~

-1t e

bull I a li o

fWvfIIIacute)iC-Q ~~~ YQo l~

~ A~~~ e ~~

- _~_ --shy~

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 8: Calculo numerico   1991

bull I a li o

fWvfIIIacute)iC-Q ~~~ YQo l~

~ A~~~ e ~~

- _~_ --shy~

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 9: Calculo numerico   1991

-Se

I

b

3_ Su~rrk te~ ll~ ~J2NUOD ~ (0 1 e o I)i~ f) eacute CO~~ eJvA Cq h1 Il~ ecirc f eacute WOVOtvVA QAN (0) oJ

_ Se -Rta) -M traquo lt o -rgt3 UfNO tltniCQ ~ ~ YQl)t l~ltV~ _Se -(Q)I( -Ccedilto) gt0 =]gt0 ~ ~~~ ~~ l~~

~ ooacute~Joo 4~ oo~ ~ ~ o ~G~ D 3 0Jo ~-Q-CO ~ ~ bo(O ~QCoCoiM

1)- -t iacutet) ~ laquo - fWMt 1 lt-l

~3_ fJM)L = o

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 10: Calculo numerico   1991

~ I

l-) t k )

--~~----~-_- ~

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

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------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 11: Calculo numerico   1991

O~~CQ CoW fWJmiddot ~ ~ -

~Je ~-

~

S1b~= G~1middot 7 Q

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 12: Calculo numerico   1991

11(51- ~ ~-ltb ~~9Otildep ~ ~ocirce i ~ ~ ~o~ ~ I

~(amp ( amp ~gt L -lol~-t~ ( -l+1 i ~~ ) ] JIacuteJm~

~~4 Q-i- i634~--~ =0 ~ = ~

~~u ~3ccedillt~ cJ~~fQ

(~ 1tlCJo o~ ii = 1Pli 3 t ltl ~ 59 e ~o~ 3 Q tgtamp~ f ~~ )

J

2ft = 3 i453J 7$iL ~1 ~ ~ ~3~

middot~1 = 11

b tfl~ ~~ ~~

Q ~Ica ~eacute3

3gt~SE e)11

e-

~V ~l ~y= Ih~~ ~ ~~ - raquoJl ~ l~

~~0Il ~~~-lt bullbull k-- ~J ~~ f 4

j3~ecccedil~QJ ~_ amp2 ~Ml-~ 3

3gtlamp8t ~4

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

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ftn 3) a44 ti--J ~t8

PROCERGS

----

-

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i shy

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ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

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QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

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~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

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f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

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t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

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30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

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o

~J~~r J~ 7f$

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2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

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r-- ~~~ -_~~_~~~ -~-__-

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t ~3lgtIi

J 20 21 2iacuteZ

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2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

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I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

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iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

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11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

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f0C 4odmiddot o

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-

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jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

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t ~ ~ clt ~l e Yfuacutel~

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_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

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1 ~iacute)5

1amp815

11~lZ-S

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J

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OI CQj)4 021

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01~ S81

t o) ~06

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iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

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~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

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I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 13: Calculo numerico   1991

-- -----~

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

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ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

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t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

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~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

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~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

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~~~ ampultJllr-~St ~ ~middotl

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~~~ n~k 1

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f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

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YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

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o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

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2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

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t ~3lgtIi

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11 ~

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2shy

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I __ bull

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iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

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11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

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O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

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OI CQj)4 021

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O)6~ 323

01~ S81

t o) ~06

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l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

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i 1 25

t~S

li 3-=t-5

O 5 t bL~

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~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

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I

ccedilL~) to~It h-o) ~ I lt--cf

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~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 14: Calculo numerico   1991

)~0~tt~~A~eacute~ ~~)

-3 ~ ~9r= i3 ] ~~~~1~ = ~E- L-l-tJ

t 6-~1 Rt eurot-1o)

~~~J RQG l~middot~1

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

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j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

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01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

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~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 15: Calculo numerico   1991

--

~ e [- ~ -1)

o~-~

~t ~ - flltfo~ ~)(ct)

_ ccedilll~) _ H4ltfi -~) b66 ~b6 f - iSo=t 8 G-

~t~)~kc ~Er6(2 e ~~CiJ o ~ do ~ e o ltt ~ioJ VVQ -Q~

dJgt tgt ~SE e ~ 7 e

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 16: Calculo numerico   1991

----------------------------- -------------------------------------------------------SIQ4~------------~----~~-~~rzcJ------------------ --~--- middot_~~___ iacute~Oacuteg-~-~--~a--A---~~~J---------- ------------------------shy

======-middot------~==~~====~=r=~~=~=fu~~~~=-=~=~~l_~~___~____Q __I_Cl__I_2J__lA_LT__LI_~--~yo---~~1i~_ -ii-~-------middot------------middot---------T------middot-----middot-middot----------------------------___________________________~-~-L-Q--~--k--~~--~-~~-4__

=~~==~===========~===~=~~=~~=====~==~=~~=~=~= ---------------__---- ~-----------------------------_------------------------_-

1 _____________________----gltl--Jf-lft--rtJ-t-2Jt~=_9~_ecirc__________________r -4

____ _________________ ~------~----------------r _a 0----------------------shy__________~-l----S~plusmn- ~plusmn-~---~------------- _0_ _~_ --------------------eell$~~~~~~~~----------middot---------- ---------__------__----------------------------_ _--~--_ __-__--------shy----tYAi~--~--~6acirc--CcedilQ~--~--llCl--- -------------------shy

===========~~=~==~~~================================================= ----------- --------------------------------k------t-middot------- ----------------- CL-l= Q ~ 1- Q 1t 1

==~==middotb~==~==K==iZ~~~-=~~~~~=~~===~===~=p(~~=-fL~--~---~--IIo~----------------------------------------------

=================~===~l~==~-==~~~=~~=============~~=~~l~i=~==========______________________________t ____t ___plusmn_t___________ ~jL_2M__L_-4E---------shy

-----------__ _blMgtA-___ _1QO~___5E__ ampF1~~--A---QU2I~~--~~ -~zes-t---------------------r--------- ------------- ---------------------- ---------------shy-------~---lf--~-----------~ecircL~-~-J-~-I-j~f-W ___________________________________~)q --EX1~Ie--Rh(zes----~_elfJM___________

------__----~-~~-------~-____--__---------------_ ------_--_-----------shy______ftLJ~___~t_ordf1amp=________________ _____ ______ _____ _ ____________________ _

_______ _____ I__3__L ____________ ___ ____~~ts__~~_~~_~4~lt~r-Acirc-IL-~-----) 3 ~ ll) middototl-~~I ~-- s ______________iacute ___~__f2 __________________~~~~-5---______=J~__~i~~acirc_________ _

-------------Jt--dJ--_~_________________________________________________________ _

======~~~=~=~==~===~==~~===~~~=========== ------------------- --____ _Ccedil9Ib___Qe__ fUJ1WQQ____ ------------aimiddot-middot--middot---------shy------------------ -----~_--------r--~rt--t~-e+-t~t-r------------shy------------------jJll----~middot-~--t--1--~- -J-~--o~-~--i--lt3h-middot-t---------------------------------------------__---~--------~----------------------------------------~----~----k_i---~~---~=e----t----~~1(-t~---------------

1f~ + a - t4 J2 -+ 24~ - ~C) 1unl- O) fIt )( t-4)

11 shy- t4 ~ O(2 o

24 ~ lt - i) (- lO) - 140 -+ ~ ~odL ~ ~~f((IIOl ~O~ Q aacute amp 4shy

Qh- 1

tQf I~ li3 11~ 1

dego=fotilde agraveCI ~ O-~l ~ l ~ l ~ I ~ I ~ ~= -~-4

01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

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t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

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ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

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iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

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~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

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a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

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a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

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bull t bull

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l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

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~~

o~ =0

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f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

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Page 17: Calculo numerico   1991

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11 shy- t4 ~ O(2 o

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Qh- 1

tQf I~ li3 11~ 1

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01 ~1 LI - L mM ti ~ I I-Ti~) IS~ [V3) ltl11)00 -10

lC1 ~ raquolNMC O) Jiacute1I) ~~- la 7 ~ ~ s ~~ o) 3J Tt1 2aegt r+ J et ~ Q 3J t4 gt 1-48

~ ~ +-~8 -l-I 4ocirc s ~ ~+J -S toshy

~(Iacute~~(lt) = ~-f - acirc~3-+ 3 J 3T ((t _ i~68 L + O 3f 36

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

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~tf~ Q~4 ~ lo

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~

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QU t~ l ltlh 4- o(gt1t1 b1 -

=

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-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

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J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

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5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

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Qhtamp NKAgrave ~) INQ

-------

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e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

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f o

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~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

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~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

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_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

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L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

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I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

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o to 1 ~i

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totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

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~~~ ampultJllr-~St ~ ~middotl

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f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

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( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

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tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

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to

ccedil d Rlt h ~~

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---

a ( 1- ~o) ( ~ lt0)

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ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

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14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

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255 01l~7t l~) 5 1

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~

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ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 18: Calculo numerico   1991

(3~ ~~~~ ~z + ~ ~i + ~J 3

A ~ ~ IV~ ifJ la ~ -I- -t Ii + ltl] o~ l~ 108915~

~ 13

t~~31I~ ~+1~ l~ +l~~ c~ ~~~~~ (j3~~ ~l333tocirc4~4a

3) fl44 8ge ~99

~) Qegt5~ -fae

ftn 3) a44 ti--J ~t8

PROCERGS

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

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~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 19: Calculo numerico   1991

----

-

)rt~)

~ --i

~J -O-5

t~ - 01- 3

i shy

~3 o

ti ~llbe5 4- 21-3ZB

~3 ~1-32

( if4 2 -=t3~J

--~~_--- ----_~_~---_ _------ ---~

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

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j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

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~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

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~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

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r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

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t ~3lgtIi

J 20 21 2iacuteZ

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4 1443l

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O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

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tagt (L lS t ~ 1 (()

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__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 20: Calculo numerico   1991

I

r~~Jj~8L 1~

ltlu ~L -+ 0 i J + aVCf =J~

) ~~( ~l t o~2 2t1 Iacute bullbull oL~1 n-a

~tf~ Q~4 ~ lo

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

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o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

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r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

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--r LIr

fI

fFI JJ

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~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

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) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

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-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 21: Calculo numerico   1991

_ Q o ~ k ~ NCl~l o~-nOd-~ agraveo ~ 3ltgt JIl- do ~ Q12

~~J -- 0 1 -+ Q tfl b

=l 3

~I

~

~~

~ l~

QU t~ l ltlh 4- o(gt1t1 b1 -

=

eurogtX ~u1gt~~oo I ~ ~09~ 6lt5 = b-= l99

-Si + ef8= - ~)6t -~ j 3 99

S~ - 5~r ~ P (1r ~

i~ iacute ~] o~atildeo ~da 3~~l2-~9

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

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-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 22: Calculo numerico   1991

J ~- ) 1lt1 ~ 00 OtildeO LU lt7 FO ~

gt i~9 - b ~~3-- -=I bull ~199 ~ c3f)~ - b I -+ 1-b =lt 3 =) Ocirc

9 i~9 - s a9 g ~ 1id6 St - 5~ 3

5 j~S _ t3 3)~lt3 -- ~ ~)3~ - 3~~ yl 5a - 6j +b ~ - ~

dt ~COfdo o QoI(I~cioeoN

2Sf ~~u )o- OIO~r 3

~9 OO tf ri 3

_3) 9 ~ o o3 f - ~

~t - foi -- tacirc- ~ 3

) ~ - 51gt- = 3

Lotilde- - ltOi + b acirc ~ -1

1ltr - 4j -tB b-= ~

n I 1~ _ 4 3~ 6 L -l - 0 middotH - j h 01)0

WoOacuteD Oacutei~o ~ l)l~llDo ultgtP - r eo t~ - -ow

~ io~ l~~(OIO (v- Y-t lJ-) - ~(i)J

o i o 1 1 i ~ J

tb-o ~ to ~(-S ~ d- lt -oeb)J

~ =J iacute ltgt 5JJOraquo ~

EO~ 1tQIJO tgtLW~IacuteIIO VI (-NJ5S - ~E)EL _ ~~F coetA Ee~AReoamp-

~Q o ~~~

~ ~l + (~~~ 4- - bull o~ t = 0 1

) Ql ~ 4 Q~t~ -+ 0Y~ = b -t

I ~~ ce +0 1tgt ~ - Q (f ~ b ~ 1 L l- ~

S~_Je - ~~~IgtW- )0 ~ltl rf~ o

Qhtamp NKAgrave ~) INQ

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 23: Calculo numerico   1991

-------

)

e otj -= Gij

i fj a~i

-~----~--- -~-

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 24: Calculo numerico   1991

lli iacutehLo Nl-1VIilto ~

~eooLuqotildeo de SeffiOS deuro ~UA~ L~(l

G~~ccediliacuteo ~ f~~QPt~ _~Q o iJ~~ 1 X- ) ~ ~-1tijQlotildeo fi~ ~~ ~~ltYOJ fi CO ltIC =~ +11

tl~ ~ - ~i

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 25: Calculo numerico   1991

t 1 (~_ ~~ ) A(f - A~ 8- A~ ~a a

iacutegt- _ i + n 7 ~ - l A

3 ~~~ _ Ck~-~ o ~o ~ Je Jlt9 a WltO~ampotildeo ~ h~-e lt)I~m= do1gt gtJ1IONVll~ l-e o JJtvru ~ ~ COI(dlQiO~ 0 ~Q~~ ltke ~ ~~ e-I ~gt-ampt~ cq~ ~~ordfA(~

61~Oj ~~I~i OlOO5~~osHc1)

SMS6

0005043 j O Sti-09

j= 5C 1cA9 ] i ~ f-~5) 1 90=- -65) 5~41 -gt

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 26: Calculo numerico   1991

p39

00051-043

01 oo~ gt f = - o00065 t 4 ~ o- j= - 0 IA ~~

~l1 k 6 9j1 0100 ~4 9 ~bt o) l49 ~

WNOMll

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 27: Calculo numerico   1991

~ttt-) -d ~(~) afhO(AgraveJfvOM~ de Q1 ) rvv

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 28: Calculo numerico   1991

- -

2- ~ 1 i tt o

f o

f Acirc o ((f= ~~ t~ Yi ~ i - ecirc(i

-

t~c ~ all iIacutej

Qo f(f(J 00 lY1-1- ) for~ 0~ k~NIONVAtildeltl ~ ~

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 29: Calculo numerico   1991

~lt~

L~) ) o(Ll Co 00 ~ ~~~~ -) ~~ [Jfj G l

~~ ) ) Ltt) ~ l (~ )lL ~ti ~ o ~lt)l-(L ~ f j

~ +~ Lc-t) ~ o fi ~ ~ ltl6L) o =-- ~i ~

) I I - -j

~t) = 1l-~) l~1C) 11- ~~- L ~_~-) ll( -1l-gtll )( _it) (j)tcmiddotC( )

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 30: Calculo numerico   1991

~~_~ Q ~~~ampo ~cIJ lt1~ ~~ ~ rrr-oJl ~~N6J dt

J- Z~ I j~OOkagrave4 e3 laquol ~ ~t2-~ocirc o 20 C1 3t4~5 ~~ fcampL ~ ~~~~~ ((1- 1 ~Ilt oloro56 ~l 2- ~lb -o) ()gb~Q

~ 3 ~18 _ 01 95()S- ~lltJ 1l o tI) t L1 llt-)+ l ~(-)~ ll-J+ l n+~ f()~ 3 lo

~ht) lv(~h IUumll-)~ L2lt)-I- L-)t) +1--4 uumlc) 3

P(il3)~ll))+ -t~lI)Llt(lt3)~ middotT tle 3

7I_ ~i ~- ~z CL- (3

o b~)= ( it3- ~J ) lt23- iacute) lltJ- (~) middot~(2-O)~ ~ tO _ ~Jq) -O - tI amp) L 20- ZJ6 )

L2(l3)=~ L~Ll3) ~

fb() Lol~)+ ld~)+ l2ll)+ l3t~J-= O088oto

~ ~~ o~ I ~~ o aQ o ~~c~ dI

~~ ~ ~~~ ~h ~ ~o~ ~ t~)

_shy

~b IQ -11 ~~-a ~)((

ai i -- 5 ot 5 (~~ )

~ 2 i 0 lI- bull ~ltt- lU) l 01-- t ) bull ~ l o) Clt -l~iJt-11 ( l-2

~-~i) l ~= t~) middot~t~middot l-ecirc-(jJ1t~2-11

L~-t-l ) l~-d ) (-tL)

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

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~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

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I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 31: Calculo numerico   1991

ltgt tlt) l-~J l Y- ~z) ( t$- ~V )

cC-o-(fd( ~ middot-l4 ) (~O f~)

li~) (J + 4~+d

L2Lt-) (

l1tQ+c ) d 4-1- + ~

~l~raquo- l-ecirc 40IJ

I 1 ~ -~) _ 0 4 J~ Ja _ Q) (Slaquo + S)3~amp4

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

-~

15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

YtJ - --shyPl2o~) 2-0 o~~ MIJ

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

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O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

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iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 32: Calculo numerico   1991

~~ )~~) )

~

o to 1 ~i

2 ilt tt33 t44

S f5

o ~ QN-~~ r(~IlA O~~ do OoacuteeJbSe Q)CfJM~

totilde-~ ~ de ~~ ~~~~ C1 ie dNb ~

~ ~I ~

~~ rvoltio to ~Of) - - shySe

~~~ ampultJllr-~St ~ ~middotl

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

~~~ ri Rt) (ll~J I l(t J [~+11l~ ff)lJ [ i ii- 3 ~ lii ICli +1 bull 1(1J ~~ J30 0)(~ ~lt o U1

14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

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15lO~ ~

( ~O LO -

30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

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YYJOtilde~lfM 20 I 8Lv ~l ~ e

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~ de l~ro2gt agrave VQltaacuteBIJvv--o

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o

~J~~r J~ 7f$

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~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

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CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

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~ 3) 1-6~

4 1443l

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O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

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f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

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jley

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tagt (L lS t ~ 1 (()

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O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

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1 ~iacute)5

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rt _ -o 66 2-95

O6~ Dt~

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4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

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= 7 (o ns)

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comiddot

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_ 0

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ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 33: Calculo numerico   1991

~~9 CJotildel~o JAJ~~ltU)

~~~ n~k 1

(J j Aji Kji -(~h~ febOSshy

f i)S L ~55 oIU3 2)~~~~ lt ri 0 f t 160 _oISH~ ibo02~-ik l1b5

~() f AQJ _ 02811 ~It-O

t~fltIIW ~t5

leuroO 0)133+

lt406 3

~~cJQckAgrave laquoJ ~ ~ O(l ~ l oJM BgtrQ~ ~- ~ ~ ~~ ~~

( ~~l~

i~~ ~ )Cf

joO~4~t ~i~Z 2 ~I

ftl~1 t lz3 iL9 ~5

jltb 0amp

lt4f 6~) middotmiddot-Ii ) [lt-W)atildetti Xi]

( i-+i I ~1 ~-j)A-6-Dlc

l13-o) Jtl-o)4 (~ - 4) I(J-o f) ( lq-~O) b- 2lc- J~) Its- 2)~l ~t-Ocirc) Il3-Z)= rg

(t_4~) b-3)H shyl 2S - 2f) le 5-~ 49

( 1 _~ e~)f- s)

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

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14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

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~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

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15lO~ ~

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30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

~)~ OJ ~l l-OgO JZ5)7 o

YYJOtilde~lfM 20 I 8Lv ~l ~ e

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~ de l~ro2gt agrave VQltaacuteBIJvv--o

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o

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2) t(YO~ - ~Ikk

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O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

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2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

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-

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jley

lt1~ ~

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O ~250 UacuteI o(3~~

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(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

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rt _ -o 66 2-95

O6~ Dt~

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4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

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--r LIr

fI

fFI JJ

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1 o) ~l li ~i i b~i i

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11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

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Z

~Oraquo hO lS

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i 1 25

t~S

li 3-=t-5

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~~~ QOf~~CONY

~ ~WNVgt~

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1~5 Q l dt41t

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I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

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euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 34: Calculo numerico   1991

I

ioacute~ ~ r~~oltgt i~~Uuml clt JzwJ~ c J~~~ Y

QIN~ )J6~

VtJ )+ ~o) Ajo (l(-)(1- (J) A) f -+ -lo (lt-lld( t- IJ bJQ

i b Ij~ rylt4 ~

~o O S 10 O

tll to 151 -u5 1tz W lo 1~ ~ -~ 3J ~ ~1 --

- to 5~

to

ccedil d Rlt h ~~

3 1gt li

-~~

---

a ( 1- ~o) ( ~ lt0)

6gt1 OO

ct l~- middotw)(~- lo) = l (J2_ ~o il-)( IX - lto) ~ r _()L~_(20~ - zCKJx)

~l~) - jo-t lampAol [~) lIacuteol +(t--~)(lI--~) tt) I t a J+ T

lgtt-1lo)C liacute-yJ l lt1- ~-i ) L1e )(-24 toJ

N

--~~ ~-~~-~_------------------

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14 10 I tI 49 01- o )33 08l1 lO 1 lt-I b2

J) ~d h 21-0

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~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

-~Is Ul - ()) l~)

~

~ JgtQ )l A~~j~ ~Ji~

lO G o 1deg ( O _2

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30 ~ + ( () -o)(~ -fJ) ( ltl -zJIv ( l ~_o)( $--lO) )(0 ~_ (-tecirc) (te-O)5 +

y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

6000

f lt1--)

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YYJOtilde~lfM 20 I 8Lv ~l ~ e

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o

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2) t(YO~ - ~Ikk

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~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

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15 o~ [ ft 4 (~ fJI- h~ ~~J

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-

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2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

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bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

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Dh

08 30

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l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

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bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

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~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

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) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

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Page 35: Calculo numerico   1991

--~~ ~-~~-~_------------------

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bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

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t

bull (-1- ~ ( ~ j V ) ~

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(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

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T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

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~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

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Page 36: Calculo numerico   1991

~~ampamp~~ ~~-~~ Jo f 00 YN5-gt$Aacute ~ -e

~IQO~h dLo~ ~ ~)o ~ 1

255 01l~7t l~) 5 1

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y~) Ot- ----T 3~~~Jo lo

2 O lOacutes

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o

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l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

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o~ =0

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ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 37: Calculo numerico   1991

~ de l~ro2gt agrave VQltaacuteBIJvv--o

~euro()N~tto~~ lo~lt) ltk oacute-ltbC) bull 10 co wrMJoloacuteotilde ~ oltgt ww 2

o

~J~~r J~ 7f$

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

_ ~-5__OIpdegLl96 - -1 a~ degll~~ ~29 tlTS lt) ~T9 3t3

_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

i~5

J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

O)6~ 323

01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 38: Calculo numerico   1991

J~Q bOacutehQuuml doo o~t-o do uh~

~ Jf[iacute-1L~ ~ middot 4 J1- J o o

c

~)~~~ ~~w

~~

CfffiFCJ~ 1gtf5 lN~GRMS (rm 1~) ~l)tta~ltb

2) t(YO~ - ~Ikk

toacuteMIo_h~ ~ I~)~ ~l ~+~(l1-t+~-)+ f J

miodc lti~ 1lQW~) _ eoes )

-2

r-- ~~~ -_~~_~~~ -~-__-

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

------ shy

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_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

11~lZ-S

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J

~P -tF O~SP4 O 66 3Q9 --shy

O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

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01~ S81

t o) ~06

~ ~8-1 45

iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

~) at~ o

~~ ~~clo

o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

1~ 3 4 t~-3

1O 3 )6 2~O1

li ~) t4 laquo31

L( 4 5foJ ~I

~7gt 5 O 3 lz

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

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comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

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I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 39: Calculo numerico   1991

~~ ~OjJro QoIYYI QQ2~~laquo CJ~ J3lt-)t

~- O)l 19ltrt

t ~3lgtIi

J 20 21 2iacuteZ

11 ~

~~JJ 34ll-l-3 ~

~ 3) 1-6~

4 1443l

) 56i9~

otilde)034a~

O~ ~ ~41H ~~3+ 2laquo 4)4 ~ ~ ~1Y3~22) ~

~ ilbS~

~) ~ ~OI T-= Ol (tt~(e~lt+(J+f)

2shy

t- ~ 0IOS t3i~ut 2l3)J~21t1JK3~$1-- $) ()31-ZZ t) 6Jo ~ 9

~4cC ~T ~ o) 513-=Jmiddot ocirclt

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

~ 40 ~1 ( - 4 ~~

t ~ ~ clt ~l e Yfuacutel~

Q~ ~ tl~) I lt ~~-~ )E-

tagt (L lS t ~ 1 (()

shy

Qci9euQo JU~

~ GlCcedil) t ~~ lccedill f_lt )1 1

_to l ~ ~ ) 1 ~- s ~ ~ -= i t a Z 1

__ _ _P - - - --

(

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_--- ~ kt ~lL) ~to I l6( gt3middot1

O ~250 UacuteI o(3~~

o ~9SQ r=JfI 61-1

(

Q i tlS l 3tS

(V~~S e I 6~ 5

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

J laquo3iS

1 ~iacute)5

1amp815

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O6h~5 O b3h Mj5

OI CQj)4 021

O ~5( ~t 3 6f+OSQ)

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01~ S81

t o) ~06

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iacute (

l~

H

rt _ -o 66 2-95

O6~ Dt~

O roJ6 25

4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

[13

--r LIr

fI

fFI JJ

0636 ~~ o~bQJ5O) 636 295

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o - 1 c shyf 3(1

~Io~ fI J ~ ~ u~

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1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

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t~S

li 3-=t-5

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2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 40: Calculo numerico   1991

I __ bull

ltP eooo O ~ NO-la~) e ~ ~OJQ t ~~() o ~~~ jt

-EJlo ele ~IV~

iacute ~ (~- 1() tNgtlt e~l L~ [ lo ItJ ~

~IYJ~ d~ Ccedil)vvv~~OIY ~ ~-t 4 (~iTf3 tts -t bull - ~-i) l (~+~ -t --- -l)+ fl J

11) -k 1 -f o+~oacuteJ ~ liAt~~ ~~_ Wgt

~9

)o1N ~Od lAb()Mlt1 o ~oacute~~ ck ~VM~~u-n

15 o~ [ ft 4 (~ fJI- h~ ~~J

1b666 Gl~ ~ I l- Cf) Qlco $tt ~ 1- (1 vl

f0C 4odmiddot o

~~ ~~ Jt~kt) ~ ~ ieacuterIltU~k ~+ ~ ~ ~

-

~ -1JL~~ J~ OacuteJY~o~OO ~Jo -= Y Jt

~i210tlmiddot shy~--+-J-(-=1l_~_~ t- a = ~ ~-f 05 T~ V- ~et4~+~1 ~ a ~ CT =- ~r0+ l432=t906+ ~J3~4( i5 t s ~ L ~ Ts ob36 51 U l shy

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

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_--- ~ kt ~lL) ~to I l6( gt3middot1

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(

Q i tlS l 3tS

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4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

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2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

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Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

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a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 41: Calculo numerico   1991

jley

lt1~ ~

g to O 11 1 U5 ~ ~ 5 ~

Ccedil)-1 ~15

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tagt (L lS t ~ 1 (()

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_--- ~ kt ~lL) ~to I l6( gt3middot1

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2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

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bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

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Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

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ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 42: Calculo numerico   1991

Qci9euQo JU~

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__ _ _P - - - --

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11 )S6~1 0)4 6831 li fi 11

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E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

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08 30

~ (10tO2) 004 0ldt l 010 i

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a ltl = O a l-z) -04

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ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

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Page 43: Calculo numerico   1991

t J 4olbbll 4-4 i~ shy1 8-ts

iHl1 i

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4f(~)_1f ~o)- 4flvs)- 1(f)- _ o63Sf

3

= 7 (o ns)

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fI

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2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 44: Calculo numerico   1991

~) at~ o

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~IO 0362 11 o) 04 14

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~I~ SO~=t21

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) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

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i 1 25

t~S

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~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 45: Calculo numerico   1991

1 o) ~l li ~i i b~i i

1~ 3)4IT~3 deg1~4~ o03T6Cf

~IO 0362 11 o) 04 14

~d O) 1360 O04$tf

11 )S6~1 0)4 6831 li fi 11

~I~ SO~=t21

~

_Z

) q04S~l- o) S23~ 0 ~3- )~ t T lt-_~r2 (

Z

~Oraquo hO lS

-= ltJ rZ CO

i 1 25

t~S

li 3-=t-5

O 5 t bL~

~~~ QOf~~CONY

~ ~WNVgt~

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 46: Calculo numerico   1991

~ SlfVrot tQNO ~ ~) n 1-) h- 811- ~lL Ali ~~ c~ ck b)JO Je coJQ -u~~~_

a~ -l-I)i~qru ~~~ o

comiddot

1~5 Q l dt41t

_ 0

~ ~~ J lti- J~ o ~

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 47: Calculo numerico   1991

-shy0 -1

~ l)CcediliT

I

ccedilL~) to~It h-o) ~ I lt--cf

- z ~ -12

~Y~ i A ~J~~~ j~ ~~

euroo VVf $ tiET~ imiddot14(Ccedil) ~ ~~~ OOqli -21~3 0)08lt2A ~amp01

2 j~3 c1J)O2 Ol1

)oooJ~ 31~2 38lt31gt()ts

E lt toacute 5

r iacute() T bJ 1~) - 7il shy2 O ~2

ob~ iacuteF uacute6b3t ()b~t5 021-4 pc

OI S UacutetJI oiiacute19 Ob2l O~ tt3laquo) iIS iacuteJtJ a3

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 48: Calculo numerico   1991

~iV9i bull

Sult1otildeo NumeacuteCQmiddot agrave~ ~u()lGOO ~~~sQ)bull

bull

t ~ iacuteOt e j -+ -=t1f~ = ~4-- ti ~ o~~

j ~ ~-ti ~l f ~~ o~diJW

d~l -T 3d - l1J = o -+ Ql l f 2 Q~~

~ dt

bull

de ~ ~ltk~~ t~~ ~ LMt~QU)

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 49: Calculo numerico   1991

bull

t

bull (-1- ~ ( ~ j V ) ~

~ = ~ ~ (it-t~ ) jn+V~ ti

1l (1shy

a ~ oo 166 Ol~

Oacute~

Dh

08 30

~ (10tO2) 004 0ldt l 010 i

( I - ~ =- l(-i

ltcdgt jl jo ~ (-1-t~ ~ (1 ~ O ~ ~ (o t)

a ltl = O a l-z) -04

l-OA)~ ~~ ~ o-a ~ ( o--ocmiddot J a1J9I (l o g ~t() a ) ~ Kl= O~ bull ~-t)lt) -o~middote 2 l

ji= ~- ~O4) ~ (-028) - 166 a

bull t bull

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 50: Calculo numerico   1991

Um certo

(nltr uuml t~OOO mi~J )lH~r-a Sfl~ rf3h~ dPi cinco ~n~rlErlln~camiddotdos eSplbdi

l~L3I cidiarf d~ middotltl)-t~) Al~CcedilI1~~~ ltkl ~do f~is eccediltJiJiJuacutellicuuml possJgtvel Of

lr~rfSsi dade

d i ~~ 1 eacutetmi)nta do qt~ ()Jtmiddotrc i

(Hd CC1ndY o depv6s1to cantlal

~AT~~ X~ ~) jl ~JOuacute (~i

T ~ L J

~t ~Uacute(~ i(tj(1~ (uacute ~~r

li Jbullbull

_ rf~ ~~wt tJI~ f)i(HI ~

~~) J eacute D)t~ i)t~~~ (ti)

~ middott iacute~~t t~i i ~Cmiddott fli)( i~)

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 51: Calculo numerico   1991

~~

o~ =0

~~

f) I Q o e Giacute I o f((QJN)

COf i (00+Q1 ~L- j~)---= ~ ~

ce ~ ~ lQ+ ctL~- j ) 2(

)ClJ - LO

Q1~ o J)lo~ e eu J Ej i = Z +Qi

j l l~ ( ~+ QLltl - jd= o

~ ( jc = iQ~i ~ ~o (lodt L IC- ) ~ = o

) (nH)c + Qi 2 Ui ZJi

l 00 ~ liacute l + Qi ~ lt tli1

~-~-

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1

Page 52: Calculo numerico   1991

2j~ ~ (YL+)-t QL ~[+ Q ZlliJ

z ~~ Qo Z1Iacute(+ Qii~+Qe z~3

-Z ~~jt ltlo 2~+ 0I ~c(()+ Q~~~1