Solucion metodos anteriores

8/18/2019 Solucion metodos anteriores

1/48

Solución Nº 1

Caso 1

1.000 0.500 0.333 0.0000.500 0.333 0.250 1.0000.333 0.250 0.200 0.000

1.00000 0.50000 0.33333 0.000.5000 0.08333 0.08333 1.000.3333 0.08333 0.08889 0.00

1.00000 0.50000 0.33333 0.000.08333 0.08333 1.00

1.0000 0.00556 -1.00

1.00000 0.50000 0.33333 0.000.083333 0.08333 1.00

0.00556 -1.00

x

-36.000

192.000

-180.000

Caso 2

Ingresando Datos con 3 decimalesy redondeando a 3 cifras significativas

1.000 0.500 0.333 0.0000.500 0.333 0.250 1.0000.333 0.250 0.200 0.000

1.00000 0.500 0.333 0.0000.500 0.083 0.083 1.0000.333 0.084 0.089 0.000

1.00000 0.500 0.333 0.0000.083 0.083 1.000

1.012 0.005 -1.012

1.00000 0.500 0.333 0.0000.083 0.083 1.000

0.005 -1.012

Error : 1.20% x

-39.757

214.448-202.400

Comparación de Resultados

!sul"a#o 1 !sul"a#o 2 Error $%

-36.000 -39.757 10%192.000 214.448 12%

Matriz & Matriz '

Matriz & Matriz '


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S! (u!#! a(r!ciar !l !rror #! los r!sul"a#os cuan#o s! "ra'a)a con 3 ci*ras si+ni*ica"i,as


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CES /E EN&CN /EC&

a"ri & a"ri x a"ri '

1 1 1 2 1 3 x1 0 1

1 2 1 3 1 4 x2 1 1

1 3 1 4 1 5 x3 0 1

1 0.5 0.3333333333 00.5 0 0.0833333333 0.0833333333 1

0.3333333 0 0.0833333333 0.0888888889 0

1 0.5 0.3333333333 00 0.0833333333 0.0833333333 1

1 0 0 0.0055555556 -1

x3 -180

x2 192

x1 -36

CES /E EN&CN /EC& &/& & ES C&S SNC&&S

a"ri & a"ri x a"ri '

1.000 0.500 0.333 x1 0 1

0.500 0.333 0.250 x2 1 1

0.333 0.250 0.200 x3 0 1

1.000 0.500 0.333 00.5000 0 0.083000 0.0835 10.3330 0 0.0835 0.089111 0

1.000 0.500000 0.33300 00 0.083000 0.08350 1

1.0060 0 0 0.00511 -1.006

x3 -196.946x2 210.181

x1 -39.507


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a"ri n,!rsa

1.833 1.000 0.500 0.333 1.000 0.000 0.0001.083 0.500 0.333 0.250 0.000 1.000 0.0000.783 0.333 0.250 0.200 0.000 0.000 1.000

1.000 0.500 0.333 1.000 0.000 0.000f1*.5(-1)+f2 0.000 0.083 0.083 -0.500 1.000 0.000f1*.33(-1)+f3 0.000 0.083 0.089 -0.333 0.000 1.000

1 0.500 0.333 1.000 0.000 0.000f2/.083 0.000 1.000 1.001 -6.002 12.005 0.000

0.000 0.083 0.089 -0.333 0.000 1.000

1.000 0.500 0.333 1.000 0.000 0.0000.000 1.000 1.001 -6.002 12.005 0.000

f2*-.o83+f3 0.000 0.000 0.006 0.167 -1.001 1.000

1.000 0.500 0.333 1.000 0.000 0.0000.000 1.000 1.001 -6.002 12.005 0.000

f3/.006 0.000 0.000 1.000 30.303 -181.562 181.453

f3+-.333+f1 1 0.500 0 -9.101 61 -60f3-f2 0.000 1.000 0.001 -36.305 193.566 -181.453

0.000 0.000 1.000 30.303 -181.562 181.453

f2*.5-f1 1.000 0.000 0.000 9.052 -36.263 30.242 75.000

b 0.000 1.000 0.001 -36.305 193.566 -181.453 408.0000.000 0.000 1.000 3 0.303 -181.562 181.453 390.000

747.986

b X

0.000 -36.2631.000 193.5660.000 -181.562

Matriz &

k(a)=| |∞*|A¯¹|∞


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auss-S!i#!l 3 ! -0.2 "0.1 ! 7 "0.4 ! -0.1 "

3 -0.2 -0.5 -1 9 1 ! 0.2 "

0.1 7 0.4 0.5 -190.4 -0.1 10 1 73.4

1 0.2 0.5 6 12.5

3 4.26 -0.2 -3.240 0 0 0 0 0.1 4.26 7 -3.241 3.0000 -2.7571 7.1924 1.0759 0.4 4.26 -0.1 -3.242 4.3736 -3.2646 7.0248 0.8778 1 4.26 0.2 -3.243 4.2458 -3.2391 7.0500 0.89624 4.2578 -3.2420 7.0477 0.89455 4.2566 -3.2417 7.0479 0.8946 #$a &ia'. = 266 4.2567 -3.2417 7.0479 0.89467 4.2567 -3.2417 7.0479 0.8946 #$a r#to = 2.3

8 4.2567 -3.2417 7.0479 0.89469 4.2567 -3.2417 7.0479 0.8946

10 4.2567 -3.2417 7.0479 0.8946x ;

auss-S!i#!l 8 ! -2 "4 ! 10 "1 ! -3 "

8 -2 -2 -1 20 2 ! 1 "4 10 3 2 51 -3 5 -2 402 1 -3 3 -10

8 4.26 -2 -3.240 0 0 0 0 4 4.26 10 -3.241 3.0000 -2.7571 7.1924 1.0759 1 4.26 -3 -3.242 4.3736 -3.2646 7.0248 0.8778 2 4.26 1 -3.243 4.2458 -3.2391 7.0500 0.8962

4 4.2578 -3.2420 7.0477 0.89455 4.2566 -3.2417 7.0479 0.8946 #$a &ia'. = 266 4.2567 -3.2417 7.0479 0.89467 4.2567 -3.2417 7.0479 0.8946 #$a r#to = 08 4.2567 -3.2417 7.0479 0.89469 4.2567 -3.2417 7.0479 0.8946

10 4.2567 -3.2417 7.0479 0.8946x ;


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-0.5 z -1 = 90.4 z 0.5 = -1910 z 1 = 73.40.5 z 6 = 12.5

-0.5 7.05 -1 0.89 = 9.00000.4 7.05 0.5 0.89 = -19.000010 7.05 1 0.89 = 73.40000.5 7.05 6 0.89 = 12.5000

-2 z -1 = 203 z 2 = 55 z -2 = 40

-3 z 3 = -10

-2 7.05 -1 0.89 = 25.5469964373 7.05 2 0.89 = 85 7.05 -2 0.89 = 47.431956438

-3 7.05 3 0.89 = -13.18798004


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-2 z -1 = 123 z 2 = 55 z -2 = 35

-3 z 3 = -10

-2 5.61 -1 1.45 = 12.00023 5.61 2 1.45 = 5.00005 5.61 -2 1.45 = 35.0000

-3 5.61 3 1.45 = -10.0000

-2 z -1 = 203 z 2 = 55 z -2 = 40

-3 z 3 = -10

-2 5.61 -1 1.45 = 12.00022209093 5.61 2 1.45 = 55 5.61 -2 1.45 = 35.0000486453

-3 5.61 3 1.45 = -10


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a b 0 0& a b 0

0 a b =0 0 a

N:r#!n #! la ' c

a 3.000 0.416 0.672 0.672 0.416' 2.000 #= 0.476 0.294 -0.294 -0.476c 1.000 0.336 -0.208 -0.208 0.336

0.147 -0.238 0.238 -0.147

a"ri &

3.000 2.000 0.000 0.0001.000 3.000 2.000 0.0000.000 1.000 3.000 2.0000.000 0.000 1.000 3.000

"!ración /ir!c"a

? r & @?A1 B @?A1 $@?A1

0 1.000 5.000 5.000 6.000 27.000 5.000 5.3891.000 6.000 6.000 35.000 6.000

1.000 6.000 6.000 32.000 6.0001.000 4.000 4.000 18.000 4.000

1 0.833 4.500 4.500 5.833 25.167 4.500 5.3991.000 5.833 5.833 32.667 5.8331.000 5.333 5.333 27.833 5.3330.667 3.000 3.000 14.333 3.000

2 0.771 4.314 4.314 5.600 24.143 4.314 5.3841.000 5.600 5.600 30.657 5.6000.914 4.771 4.771 24.829 4.7710.514 2.457 2.457 12.143 2.457

3 0.770 4.311 4.311 5.474 23.883 4.311 5.3651.000 5.474 5.474 29.602 5.4740.852 4.434 4.434 23.112 4.4340.439 2.168 2.168 10.939 2.168

4 0.788 4.363 4.363 5.407 23.902 4.363 5.3481.000 5.407 5.407 29.028 5.4070.810 4.222 4.222 22.069 4.2220.396 1.998 1.998 10.216 1.998

5 0.807 4.420 4.420 5.368 23.998 4.420 5.3341.000 5.368 5.368 28.688 5.368

0.781 4.081 4.081 21.391 4.0810.370 1.889 1.889 9.749 1.889

D aA2'$c'12cos$s$NA1 $c'12s!n$s(i$NA1

$c'22s!n$2s(i$NA1

$c'32s!n$3s(i$NA1

$c'42s!n$4s(i$NA1

xk

& xk

B-1 & xk


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6 0.823 4.470 4.470 5.344 24.099 4.470 5.3221.000 5.344 5.344 28.471 5.3440.760 3.985 3.985 20.930 3.9850.352 1.816 1.816 9.433 1.816

alor carac"!rFs"ico #!


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12/48

D=

a"ri B $n,!rsa

1.000 0.000 0.000 0.0000.000 1.000 0.000 0.0000.000 0.000 1.000 0.0000.000 0.000 0.000 1.000

a"ri B $#ia+onal

1.000 0.000 0.000 0.0000.000 1.000 0.000 0.0000.000 0.000 1.000 0.0000.000 0.000 0.000 1.000

1.000@o 1.000 (ri

1.000 a(roxi


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2.718

0.352


14/48


15/48

a"ri & a"ri B

3 2 0 1.0004 3 2 0.0000 4 3 1.000

raslación

0.000

3.00 2.00 0.00 3.00 2.00 0.004.00 3.00 2.00 1.33 0.33 2.000.00 4.00 3.00 0.00 12.00 -21.00

0.00 0.00 0.00

"!ración n,!rsa? r

0 1.000 1.000 1.000 -0.238 0.857 1.1671.000 0.000 -1.333 0.8571.000 1.000 17.000 -0.810

1 -0.278 -0.278 -0.278 0.193 0.257 3.8971.000 0.000 0.370 -0.429

-0.944 -0.944 -5.389 0.257

2 0.753 0.753 0.753 -0.226 0.716 1.397-1.670 0.000 -1.003 0.7161.000 1.000 13.041 -0.621

3 -0.316 -0.316 -0.316 0.180 0.282 3.5431.000 0.000 0.422 -0.429

-0.868 -0.868 -5.927 0.282

15 -0.372 -0.372 -0.372 0.162 0.320 3.1301.000 0.000 0.496 -0.429

-0.756 -0.756 -6.710 0.320

16 0.506 0.506 0.506 -0.215 0.575 1.740-1.341 0.000 -0.675 0.5751.000 1.000 9.096 -0.433

17 -0.373 -0.373 -0.373 0.161 0.320 3.1221.000 0.000 0.498 -0.429

-0.753 -0.753 -6.726 0.320

18 0.504 0.504 0.504 -0.214 0.574 1.744-1.338 0.000 -0.672 0.5741.000 1.000 9.058 -0.431

-0.373 0.504

1.000 -1.338-0.753 1.000

µ =

& - µ B ,ator# G

xk

B xk

-1 B xk

G-1 -1 B xk

H1 H

2


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3.618


17/48

ro'l! o otrario o$rr $a&o #t # @o# & &i?o Aro.


18/48

ro'l!


19/48

or' $?o # ri&o> o otrario o$rr $a&o #t # @o# & &i?o Aro.


20/48


21/48

?

0 5.500000 1070.93750 754.250000 392.000000 82347.56250 1.3858 -3.66731.385807 -29.77523 30.863703 27.360367 18349.047872.101892 2.00625 61.990473 61.626730 33101.703912.068993 -0.00015 59.993424 59.782725 32393.006982.068995 0.00000 59.993575 59.782866 32393.061152.068995 0.00000 59.993575 59.782866 32393.061152.068995 0.00000 59.993575 59.782866 32393.061152.068995 0.00000 59.993575 59.782866 32393.061152.068995 0.00000 59.993575 59.782866 32393.061152.068995 0.00000 59.993575 59.782866 32393.06115

@K

$@K J$@

K L$@

K M$@

K


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3.1416 0.03750.00140625 0.00442

7.5 5 8.75 0.004375

279.1341145833 91.1458333

263.671875


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24/48

ro'l!


25/48

7.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.76000

?

0 5.500000 -6.66000 1.000000 2.000000 168.84000 7.4037 3.27897.403694 -1.13225 4.807388 2.000000 235.172957.628540 -0.00078 5.257081 2.000000 248.750697.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.760007.628688 0.00000 5.257376 2.000000 248.76000

@K

$@K J$@

K L$@

K M$@

K


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a a $ai

1 -10 x 9

rai# 1 9

1 -10 9

@ 9.09 9.09 -8.2719

-0.91 0.7281

x - 9.09 x -0.91

Error 9.00%

a a $ai

1 -10 x 9

1 -10 9

@ 1.01 1.01 -9.0799

-8.99 -0.0799

x - 1.01 x -8.99

Error 0.11%

x2

1

2

x2


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28/48

Problema 14

#$ir $a Dt'ra1 x2

Dt'ra 5xO3A4 = 54$xO4A4x

:iit# a = 1b = 2 1.25 1

28.05.25 -0.99

n" 22.75

ra(!cios

) I)$'-a$2O) Su


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-101 x A 100

-101 100


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Problema 15

Con integral asumida en P14

Dt'ra 5xO3A4 = 54$xO4A4x:iit# a = 1 28

b = 2 5.25

n" 22.75

auss !+!n#r!

i i xi *$xi ;i *$xi.;i

1 0 1.5 20.875 0.568889 11.87555792 -0.538469 1.2307655 13.3217177 0.478629 6.376160423 0.538469 1.7692345 31.690207 0.478629 15.16785214 -0.90618 1.04691 9.73717436 0.236927 2.306999515 0.90618 1.95309 41.2509003 0.236927 9.77345206

$(f(!i).i) 45.500022

n"!+ral 22.7500

x10.5P$2-1

1 A 0.5P$2A1

x1

0.51

A 1.5


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Ecuación

= 0>1>2>3

Ea$##-F?bi?ff

3

xi Cos$$i-12.(in

i xi *$xi

1 0.866025 1.2990382 0.000000 0.0000003 -0.866025 -1.299038

Gta 0.000

x( $1-xO2O$-0.5

$ n. Q *$x


32/48


33/48

Solucion Problema 1!

R-1-x Ecuacion #i*!r!ncial

"H=-1-"/! a 1.00b 1.20

Solucion e"acta

$3-xO22x

"(1.3) 1.00000"(1.5) 0.65

Datos iniciales

x

1.00 "(1.3) I0 1.0000000 Exac"o? 0.1

1.10 "(1.4) "1 0.8140900 #alor $pro"imado

%etodo Predictor Corrector


34/48

BE& 20

;o#i&r #i#ta & $aio# &ifria# $J + $=0

&o& = 200 -100 0 a# o&iio# iiia# #o $(0)= 4-100 200 -100 0

0 -100 200 0

0 1 1 1

" $K(0)= 0 :a #o$i !ata # #t a#o $=0 1 -1 1

Solución:

ia&o to&o & ifria ;tra to#

... (1)

... (2)

a# $aio# (1) " (2) obto#

;o#i&ra&o a #i'$it $ai

:$'o

$J + $ = 0

to# ro#o itratio #ta &a&o or

"

o& = 200 -100 0 D = 1 0 0

-100 200 -100 0 1 00 -100 200 0 0 1

a) M= D " =

OO = - (-(2/t2 ) M )$ - ((1/t2) M ) $

-1 (1/ t2 ) M $

+1 = OO

OO =

$ - $

-1

$+1

= OO

$-1

= $1 - t$K

+ (t2/2)$J $

-1 = $

0 - t$K

0 + (t2/2)$

0J


35/48

$(0) = 4 $K(0)= 0 $J(0) = -8000 0 4000 0 0

oroc!so #! "!ra"i,o:

0.11

n n

0 4.0000 -0.8400 -69.4215 -0.84000.0000 2.4200 200.0000 2.42000.0000 0.0000 0.0000 0.0000

1 -0.8400 4.0000 -59.4215 -0.71902.4200 0.0000 -168.0000 -2.03280.0000 0.0000 242.0000 2.9282

2 -0.7190 -0.8400 -108.9015 -1.3177-2.0328 2.4200 -201.3400 -2.43622.9282 0.0000 -304.9200 -3.6895

3 -1.3177 -0.7190 -138.4613 -1.6754-2.4362 -2.0328 120.7920 1.4616-3.6895 2.9282 -357.5550 -4.3264

4 -1.6754 -1.3177 313.2135 3.78991.4616 -2.4362 -16.9308 -0.2049

-4.3264 -3.6895 601.2514 7.2751

5 3.7899 -1.6754 -13.5747 -0.1643

-0.2049 1.4616 265.3073 3.21027.2751 -4.3264 84.5431 1.0230

6 -0.1643 3.7899 -57.5066 -0.69583.2102 -0.2049 93.6708 1.13341.0230 7.2751 -315.7377 -3.8204

7 -0.6958 -0.1643 378.0844 4.57481.1334 3.2102 267.5996 3.2380

-3.8204 1.0230 161.4083 1.9530

8 4.5748 -0.6958 9.8175 0.11883.2380 1.1334 -141.8056 -1.71581.9530 -3.8204 571.7416 6.9181

9 0.1188 4.5748 -1511.6780 -18.2913-1.7158 3.2380 639.4860 7.73786.9181 1.9530 -573.1246 -6.9348

10 -18.2913 0.1188 -773.2103 -9.3558

7.7378 -1.7158 -1838.4971 -22.2458

-6.9348 6.9181 442.7487 5.3573

si "

un

un-1

unA1


36/48

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5

-5.0000

-4.5000

-4.0000

-3.5000

-3.0000

-2.5000

-2.0000

-1.5000

-1.0000

-0.5000

0.0000

0.50001.0000

1.5000

2.0000

2.5000

3.0000

3.5000

4.0000

4.5000

5.0000

5.5000

6.0000

6.50007.0000

7.5000

8.0000

/ES&T&EN

"

G $ " %


37/48


38/48


39/48


40/48

Fo#

;o&ii Io = a

$aio ?oo'a

$ai aratri#tia

0

to# I =


41/48

Fo#

;o&ii Io = 1

171


42/48

V 8 8 V 2 A 21 V 8 8 V1

= 7 V 9 2 V 8 - 1 V 7 A 1

V 9 9 V 3 A 28 V 9 9 V1

= 8 V 10 2 V 9 - 1 V 8 A 1

V 10 10 V 4 A 36 V WW 10 V1

= 9 V 11 2 V WW - 1 V 9 A 1

V 11 11 V 5 A 45 V WW 11 V1

= 10 V 12 2 V 11 - 1 V WW A 1

V 12 12 V 6 A 55 V WW 12 V1

= 11 V 13 2 V WW - 1 V WW A 1

V 13 13 V 7 A 66 V WW 13 V1

= 12 V 14 2 V WW - 1 V WW A 1

V 14 14 V 8 A 78 V WW 14 V1

= 13 V 15 2 V WW - 1 V WW A 1

V 15 15 V 9 A 91 V WW 15 V1

= 14 V 16 2 V WW - 1 V WW A 1

V 16 16 V WW A 105 V WW 16 V1


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= 15 V 17 2 V WW - 1 V WW A 1

V 17 17 V 11 A 120 V WW 17 V1

= 16 V 18 2 V WW - 1 V WW A 1

V 18 18 V WW A 136 V WW 18 V1

= 17 V 19 2 V WW - 1 V WW A 1

V 19 19 V WW A 153 V WW 19 V1

= 18 V 20 2 V WW - 1 V WW A 1

V 20 20 V 1 - 1 V 0 A 1 V WW 20 V1

$aio ?oo'a

$ai aratri#tia

0

to I =


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ara =Io = = a

fiat

U - 1

Vn nA1 A aU -


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A 0

A 1

A 3

A 6

A 10

A 15

?$?A12


46/48

A 21

A 28

A 36

A 45

A 55

A 66

A 78

A 91

A 105


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A 120

A 136

A 153

A 171

1140


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Documents

Solucion metodos anteriores