UNIVERSIDAD CATLICA SANTO TORIBIO DE MOGROVEJO
LABORATORIO N02
DOCENTE:Lic. Yovanna Huertas Llncor
BRIGADA N 3 : Barandiarn Meoo, Amado Miguel
Briones Samam, Danny Csar
Guevara Arteaga, William Eleodoro
Hernndez Vsquez, Einstein
ASIGNATURA: Anlisis Matemtico IV
FECHA DE PRESENTACIN:
Lunes 21 de Octubre del 2013
FACULTAD DE INGENIERIA ESCUELA DE INGENIERA CIVIL Y AMBIENTAL
LABORATORIO N 02
SOLUCIN
ITERACIN a b f(a) f(b) xr f(xr) ep
1 0.4 0.5 -80 200 0.42857143 0 2 0.4 0.5 -80 200 0.42857143 0 0
ITERACIN a b f(a) f(b) xr f(xr) ep
1 0.39 0.53 -75 110.9375 0.44647059 0.1252941 2 0.39 0.446470588 -75 10058.33 0.39041796 -75.231777 14.35708
3 0.390417957 0.446470588 -75.2317767 10058.33 0.39083409 -75.461636 0.106474
4 0.390834092 0.446470588 -75.4616364 10058.33 0.39124839 -75.689475 0.105892
5 0.391248391 0.446470588 -75.6894751 10058.33 0.39166084 -75.915186 0.105307
6 0.391660838 0.446470588 -75.9151859 10058.33 0.39207141 -76.138659 0.10472
7 0.392071415 0.446470588 -76.1386593 10058.33 0.39248011 -76.359783 0.104131
8 0.392480107 0.446470588 -76.3597832 10058.33 0.3928869 -76.578443 0.103539
9 0.392886898 0.446470588 -76.5784428 10058.33 0.39329177 -76.794521 0.102945
10 0.393291771 0.446470588 -76.7945206 10058.33 0.39369471 -77.007896 0.102348
11 0.393694711 0.446470588 -77.0078964 10058.33 0.3940957 -77.218447 0.101749
El primer cuadro toma intervalos ms cercanos al resultado, resultado sin embargo de la
ecuacin 7x-3=0, debido a que la grfica no corta a y=0 en ningn punto. El otro intervalo no
converge a solucin alguna.
SOLUCIN
SOLUCIN
a) ;
ITERACIN x g(x) ep
1 1 0.25 2 0.25 0.64 300
3 0.64 0.371802499 60.9375
4 0.371802499 0.531394214 72.1344
5 0.531394214 0.426408641 30.03264073
6 0.426408641 0.491487049 24.6208831
7 0.491487049 0.449532429 13.2411237
8 0.449532429 0.475931147 9.332946179
9 0.475931147 0.459058258 5.546751583
10 0.459058258 0.469736962 3.675544354
11 0.469736962 0.462935801 2.273336964
12 0.462935801 0.467250166 1.469136975
13 0.467250166 0.464506361 0.923352289
14 0.464506361 0.46624853 0.590692616
15 0.46624853 0.465141213 0.3736567
16 0.465141213 0.465844563 0.238060435
17 0.465844563 0.465397621 0.150983827
18 0.465397621 0.465681554 0.096034261
19 0.465681554 0.465501147 0.060971408
20 0.465501147 0.465615763 0.038755366
21 0.465615763 0.465542941 0.02461593
22 0.465542941 0.465589207 0.015642448
23 0.465589207 0.465559812 0.009937189
24 0.465559812 0.465578488 0.006314003
b) ;
ITERACIN x g(x) ep
1 0 1.224744871 2 1.224744871 0.202041029 100
3 0.202041029 0.692088156 506.1862178
4 0.692088156 0.349264165 70.8070385
5 0.349264165 0.549295483 98.15607346
6 0.549295483 0.416611727 36.41597717
7 0.416611727 0.498308545 31.84830072
8 0.498308545 0.445448486 16.3948258
9 0.445448486 0.478624321 11.86670528
10 0.478624321 0.457387519 6.931497845
11 0.457387519 0.470814585 4.643065391
12 0.470814585 0.46225769 2.851879831
13 0.46225769 0.467683634 1.851109401
14 0.467683634 0.464232025 1.16017403
15 0.464232025 0.466423257 0.743509304
16 0.466423257 0.465030374 0.469794659
17 0.465030374 0.465915053 0.29952509
18 0.465915053 0.465352864 0.189879849
19 0.465352864 0.465710002 0.120809224
20 0.465710002 0.465483078 0.07668676
c) ;
ITERACIN x g(x) ep
1 0 0.5 2 0.5 0.500019039 100
3 0.500019039 0.500019041 0.003807694
SOLUCIN
a)
ITERACIN x g(x) ep
1 1.5 1.709975947 2 1.709975947 0.500222759 12.27946785
3 0.500222759 0.500019056 241.8428919
4 0.500019056 0.500019041 0.040739086
5 0.500019041 0.500019041 3.10341E-06
6 0.500019041 0.500019041 2.3638E-10
b)
ITERACIN x g(x) ep
1 1.5 1.825742 2 1.82574186 0.500254 17.84162
3 0.50025396 0.500019 264.963
4 0.50001906 0.500019 0.046978
5 0.50001904 0.500019 3.58E-06
6 0.50001904 0.500019 2.73E-10
c)
ITERACIN x g(x) ep
1 1.5 2.222222222 2 2.222222 0.500376307 32.5
3 0.500376 0.500019068 344.1102
4 0.500019 0.500019041 0.071445
5 0.500019 0.500019041 5.44E-06
6 0.500019 0.500019041 4.15E-10
La ecuacin a) converge relativamente ms rapido que las otras dos, pero todas son
aplicables.
a)
ITERACIN Xi F(Xi) F'(xi) Xi+1 Ep
1 0.8 -0.219567257 4.005973671 0.85481 6.41194683
2 0.85480996 0.009596301 4.360523869 0.852609 0.25811613
3 0.852609238 1.62363E-05 4.345775755 0.852606 0.0004382
4 0.852605502 4.67018E-11 4.345750755 0.852606 1.2604E-09
5 0.852605502 0 4.345750755 0.852606 0
b)
ITERACIN Xi F(Xi) F'(xi) Xi+1 Ep
1 1 -0.99969539 1.034904813 1.965978 49.1347336
2 1.965978105 -0.032844643 1.068612116 1.996714 1.53931891
3 1.9967139 -0.002071754 1.069684357 1.998651 0.09690488
4 1.99865069 -0.000132607 1.069751922 1.998775 0.00620184
5 1.998774651 -8.49559E-06 1.069756247 1.998783 0.00039732
6 1.998782592 -5.44308E-07 1.069756524 1.998783 2.5456E-05
c)
ITERACIN Xi F(Xi) F'(xi) Xi+1 Ep
1 0 1 -5 0.2 100
2 0.2 0.008 -4.92 0.201626 0.80645161
3 0.201626016 6.66313E-05 -4.9186939 0.20164 0.0067182
4 0.201639563 5.50819E-07 -4.91868297 0.20164 5.5537E-05
5 0.201639675 4.55316E-09 -4.91868288 0.20164 4.5908E-07
6 0.201639676 3.7637E-11 -4.91868288 0.20164 3.7948E-09
SOLUCIN
a)
; ; ;
N Xi Yi du/dx du/dy dv/dx dv/dy JACOBIANO Ui Vi
1 1.1 0.8 4.4 -1 1 8.8 39.72 1.62 -0.26
2 0.747633434 0.86958711 2.990533736 -1 1 5.98106747 18.8865841 0.248324 -0.49618
3 0.695265037 0.961302046 2.781060149 -1 1 5.5621203 16.4685911 0.005485 -0.38063
4 0.716525245 1.025912862 2.866100982 -1 1 5.73220196 17.4290697 0.000904 -0.23098
5 0.729480365 1.063947536 2.917921461 -1 1 5.83584292 18.0285313 0.000336 -0.13854
6 0.737055933 1.086388117 2.948223731 -1 1 5.89644746 18.3840463 0.000115 -0.0827
7 0.741517853 1.099657634 2.96607141 -1 1 5.93214282 18.5951592 3.98E-05 -0.04924
8 0.744152895 1.107513175 2.97661158 -1 1 5.95322316 18.720433 1.39E-05 -0.02926
9 0.745711566 1.112166621 2.982846265 -1 2 5.96569253 19.7947437 4.86E-06 -0.01737
10 0.746587802 1.114785155 2.986351206 -1 3 5.97270241 20.8365871 1.54E-06 -0.01067
11 0.747099262 1.116314091 2.988397047 -1 4 5.97679409 21.8610338 5.23E-07 -0.00674
12 0.747407594 1.117236033 2.989630376 -1 5 5.97926075 22.8757796 1.9E-07 -0.00438
13 0.747598841 1.11780798 2.990395363 -1 6 5.98079073 23.8849288 7.32E-08 -0.00291
14 0.747720509 1.11817189 2.990882036 -1 7 5.98176407 24.8907507 2.96E-08 -0.00197
15 0.747799693 1.118408748 2.991198771 -1 8 5.98239754 25.8945402 1.25E-08 -0.00136
16 0.747852295 1.118566104 2.991409179 -1 9 5.98281836 26.8970577 5.53E-09 -0.00096
x y Xi+1 Yi+1 epx epy
0.352367 -0.06959 0.747633 0.86958711
0.052368 -0.09171 0.695265 0.961302046 47.13093 8.002316
-0.02126 -0.06461 0.716525 1.025912862 7.532149 9.540699
-0.01296 -0.03803 0.72948 1.063947536 2.967126 6.297885
-0.00758 -0.02244 0.737056 1.086388117 1.775938 3.574864
-0.00446 -0.01327 0.741518 1.099657634 1.027814 2.065614
-0.00264 -0.00786 0.744153 1.107513175 0.601728 1.206695
-0.00156 -0.00465 0.745712 1.112166621 0.3541 0.709296
-0.00088 -0.00262 0.746588 1.114785155 0.209018 0.418413
-0.00051 -0.00153 0.747099 1.116314091 0.117365 0.234891
-0.00031 -0.00092 0.747408 1.117236033 0.068459 0.136963
-0.00019 -0.00057 0.747599 1.11780798 0.041254 0.08252
-0.00012 -0.00036 0.747721 1.11817189 0.025581 0.051167
-7.9E-05 -0.00024 0.7478 1.118408748 0.016272 0.032545
-5.3E-05 -0.00016 0.747852 1.118566104 0.010589 0.021178
-3.6E-05 -0.00011 0.747888 1.118672604 0.007034 0.014068
b)
; ; ;
N Xi Yi du/dx du/dy dv/dx dv/dy JACOBIANO Ui Vi
1 3.7 0.9 1.20429031 3.7 -7.18977 1 27.8064366 -0.02683 0.663331
2 3.78922965 0.878209169 1.177592673 3.78922965 -7.34174 1 28.997128 -0.00217 0.630225
3 3.87165961 0.853163489 1.14821886 3.87165961 -7.47983 1 30.1075765 -0.00224 0.594517
4 3.948185621 0.831047802 1.122248621 3.948185621 -7.60593 1 31.1518622 -0.00184 0.562327
5 4.019513996 0.81123939 1.098980212 4.019513996 -7.72153 1 32.1357728 -0.00154 0.532978
6 4.086226186 0.793381922 1.077995837 4.086226186 -7.82787 1 33.06445 -0.0013 0.506067
7 4.148807065 0.777189538 1.058960983 4.148807065 -7.92599 1 33.9423703 -0.0011 0.481271
8 4.2076658 0.762431951 1.041606258 4.2076658 -8.01676 1 34.7734677 -0.00095 0.458325
9 4.263151301 0.748921218 1.025711858 4.263151301 -8.10094 1 35.5612256 -0.00082 0.43701
10 4.315563865 0.736502207 1.011096373 4.315563865 -8.17915 1 36.3087488 -0.00071 0.417144
11 4.365164088 0.725045557 0.997608545 4.365164088 -8.25197 1 37.0188215 -0.00062 0.398576
12 4.412179809 0.714442411 0.985121091 4.412179809 -8.31989 1 37.6939529 -0.00054 0.381173
13 4.456811561 0.704600402 0.973526005 4.456811561 -8.38332 1 38.336415 -0.00048 0.364825
14 4.499236926 0.695440562 0.962730943 4.499236926 -8.44266 1 38.948274 -0.00042 0.349436
15 4.53961403 0.686894916 0.952656406 4.53961403 -8.49825 1 39.5314157 -0.00038 0.334921
16 4.578084399 0.67890458 0.94323352 4.578084399 -8.55037 1 40.0875673 -0.00034 0.321207
17 4.614775283 0.67141825 0.934402266 4.614775283 -8.59932 1 40.6183155 -0.0003 0.30823
x y Xi+1 Yi+1 epx epy
-0.08923 0.021791 3.78923 0.878209169 -0.08243 0.025046 3.87166 0.853163489 2.354823 2.48128
-0.07653 0.022116 3.948186 0.831047802 2.12906 2.935625
-0.07133 0.019808 4.019514 0.81123939 1.938258 2.661181
-0.06671 0.017857 4.086226 0.793381922 1.774552 2.441747
-0.06258 0.016192 4.148807 0.777189538 1.632611 2.250803
-0.05886 0.014758 4.207666 0.762431951 1.508407 2.083454
-0.05549 0.013511 4.263151 0.748921218 1.398845 1.935594
-0.05241 0.012419 4.315564 0.736502207 1.301514 1.804026
-0.0496 0.011457 4.365164 0.725045557 1.214501 1.686215
-0.04702 0.010603 4.41218 0.714442411 1.136274 1.580128
-0.04463 0.009842 4.456812 0.704600402 1.065589 1.484115
-0.04243 0.00916 4.499237 0.695440562 1.001428 1.396821
-0.04038 0.008546 4.539614 0.686894916 0.942946 1.317128
-0.03847 0.00799 4.578084 0.67890458 0.889439 1.244098
-0.03669 0.007486 4.614775 0.67141825 0.840316 1.176945
-0.03503 0.007027 4.649802 0.664390985 0.795074 1.115002
a)
La matriz no es de diagonal estrictamente dominante, el criterio no converge.
b)
La matriz no es de diagonal estrictamente dominante, el criterio no converge
SOLUCIN
MTODO DE PUNTO FIJO
;
ITERACIN X Y ex ey
1 1.5 1.5
2 1.25 1.23 20 21.82741
3 1.107847656 1.09 12.83139816 12.84772
4 1.041776477 1.03 6.342164582 5.608989
5 1.0152644 1.01 2.611347084 2.120049
6 1.005425063 1.00 0.978624661 0.757365
7 1.001903965 1.00 0.351440652 0.265287
8 1.000664383 1.00 0.123875904 0.092331
9 1.000231218 1.00 0.043306429 0.032073
10 1.000080368 1.00 0.015083845 0.011136
11 1.000027918 1.00 0.005244846 0.003866
12 1.000009695 1.00 0.001822244 0.001342
MTODO DE NEWTON RAPHSON
; ; ;
N Xi Yi du/dx du/dy dv/dx dv/dy JACOBIANO Ui Vi
1 1.5 1.5 -7 3 3.25 -8.5 49.75 -2.5 -2.125
2 0.944723618 1.037688442 -8.110552764 2.075376884 2.076797 -9.0552764 69.1331598 0.522064 -0.41488
3 1.000650321 1.004698115 -7.998699358 2.009396229 2.009418 -8.9993497 67.9453749 0.004216 -0.03626
4 1.000136524 1.000554647 -7.999726953 2.001109294 2.00111 -8.9998635 67.9920114 1.74E-05 -0.00416
5 1.000016288 1.000065276 -7.999967424 2.000130551 2.000131 -8.9999837 67.9990543 2.54E-07 -0.00049
6 1.00000192 1.00000768 -7.999996161 2.00001536 2.000015 -8.9999981 67.9998887 3.52E-09 -5.8E-05
7 1.000000226 1.000000904 -7.999999548 2.000001807 2.000002 -8.9999998 67.9999869 4.88E-11 -6.8E-06
x y Xi+1 Yi+1 epx epy
0.555276 0.462312 0.944724 1.037688442
-0.05593 0.03299 1.00065 1.004698115 58.7766 44.55206
0.000514 0.004143 1.000137 1.000554647 5.589036 3.283606
0.00012 0.000489 1.000016 1.000065276 0.051373 0.414117
1.44E-05 5.76E-05 1.000002 1.00000768 0.012023 0.048934
1.69E-06 6.78E-06 1 1.000000904 0.001437 0.00576
1.99E-07 7.97E-07 1 1.000000106 0.000169 0.000678
SOLUCIN
MTODO DE GAUSS-SEIDEL
N x1 x2 x3 x1,i+1 x2,i+1 x3,i+1 ep1 ep2 ep3
0 0.7 -1.6 0.6 0.96 -1.912 0.9816
1 0.96 -1.912 0.9816 0.98424 -1.993168 1.0011024 27.08333333 16.3179916 38.8753056
2 0.98424 -1.993168 1.0011024 0.99852336 -1.99992515 1.00027287 2.462813948 4.07231101 1.94809242
3 0.99852336 -1.99992515 1.00027287 0.99995774 -2.00004612 1.00002229 1.430448257 0.33787024 0.08293001
4 0.99995774 -2.00004612 1.00002229 1.000007 -2.00000586 1.00000036 0.143444366 0.00604843 0.02505796
5 1.000007 -2.00000586 1.00000036 1.00000114 -2.0000003 0.99999986 0.004925244 0.00201332 0.00219305
6 1.00000114 -2.0000003 0.99999986 1.00000007 -1.99999999 0.99999998 0.000586024 0.00027791 4.954E-05
7 1.00000007 -1.99999999 0.99999998 1 -2 1 0.000106209 1.5575E-05 1.1897E-05
8 1 -2 1 1 -2 1 7.41963E-06 4.4773E-07 1.7526E-06
9 1 -2 1 1 -2 1 3.83413E-09 1.7564E-07 1.0462E-07
10 1 -2 1 1 -2 1 5.97942E-08 1.6441E-08 2.0942E-09
11 1 -2 1 1 -2 1 6.78586E-09 4.6918E-10 1.0757E-09
12 1 -2 1 1 -2 1 2.95219E-10 7.8049E-11 1.0589E-10
13 1 -2 1 1 -2 1 2.06279E-11 1.2634E-11 3.4417E-12
14 1 -2 1 1 -2 1 4.70735E-12 8.4377E-13 4.2188E-13
15 1 -2 1 1 -2 1 3.77476E-13 2.2204E-14 8.8818E-14
16 1 -2 1 1 -2 1 0 0 0
17 1 -2 1 1 -2 1 0 0 0
I) JACOBI
Iteracion x y xi yi epx epy
1 0 0 3.75 1.8 2 3.75 1.8 4.2 1.05 100 100
3 4.2 1.05 4.0125 0.96 10.71429 71.4285714
4 4.0125 0.96 3.99 0.9975 4.672897 9.375
5 3.99 0.9975 3.999375 1.002 0.56391 3.7593985
GAUSS-SEIDEL
Iteracion x y xi yi epx epy
1 0 0 3.75 1.05 2 3.75 1.05 4.0125 0.9975 100 100
3 4.0125 0.9975 3.999375 1.000125 6.542056 5.26315789
4 3.999375 1.000125 4.00003125 0.99999375 0.328176 0.26246719
5 4.00003125 0.99999375 3.999998438 1.000000313 0.016406 0.01312508
II)
JACOBI
Iteracion x y z xi yi zi epx epy epz
1 0 0 0 2 1.375 0.75
2 2 1.375 0.75 2.125 0.96875 0.90625 100 100 100
3 2.125 0.96875 0.90625 2.0125 0.957031 1.0390625 5.88235294 41.93548 17.24138
4 2.0125 0.95703125 1.0390625 1.98359375 1.001758 1.01386719 5.59006211 1.22449 12.78195
5 1.98359375 1.001757813 1.013867188 1.997578125 1.005835 0.99545898 1.45726664 4.464808 2.48507
GAUSS-SEIDEL
Iteracion x y z xi yi zi epx epy epz
1 0 0 0 2 0.875 1.03125
2 2 0.875 1.03125 1.96875 1.011719 0.98925781 100 100 100
3 1.96875 1.01171875 0.989257813 2.004492188 0.997534 1.0017395 1.58730159 13.51351 4.244817
4 2.004492188 0.99753418 1.001739502 1.999158936 1.000428 0.99968281 1.78310436 1.421963 1.246002
5 1.999158936 1.000427704 0.999682808 2.000148979 0.999923 1.00005647 0.26677479 0.289229 0.205735
SOLUCIN
PUNTO FIJO
;
ITERACIN X Y ex ey
1 -0.2 1
2 -0.23 0.99 13.04347826 0.667882
3 -0.22023275 0.99 4.434969077 0.055659
4 -0.22270812 0.99 1.111487794 0.013877
5 -0.22209095 0.99 0.27789241 0.003474
6 -0.22224547 0.99 0.069528371 0.000869
7 -0.22220682 0.99 0.017392917 0.000217
8 -0.22221649 0.99 0.004351127 5.44E-05
9 -0.22221407 0.99 0.001088495 1.36E-05
NEWTON RAPHSON
; ; ;
N Xi Yi du/dx du/dy dv/dx dv/dy JACOBIANO Ui Vi
1 -0.2 1 -2.4 -1 -0.4 8 -19.6 -0.06 0.04
2 -0.22244898 0.993877551 -2.444897959 -1 -0.4449 7.95102041 -19.884332 0.000504 0.000654
3 -0.222214581 0.993808426 -2.444429162 -1 -0.44443 7.95046741 -19.878784 5.49E-08 7.41E-08
4 -0.222214555 0.993808419 -2.44442911 -1 -0.44443 7.95046735 -19.878783 6.66E-16 0
x y Xi+1 Yi+1 epx epy
0.022449 0.006122 -0.22245 0.993877551
-0.00023 6.91E-05 -0.22221 0.993808426 10.09174 0.616016
-2.6E-08 7.88E-09 -0.22221 0.993808419 0.105483 0.006956
-2.7E-16 -1.5E-17 -0.22221 0.993808419 1.16E-05 7.93E-07
SOLUCIN
; ;
N Xi Yi du/dx du/dy dv/dx dv/dy JACOBIANO Ui Vi
1 -0.3 -0.1 -0.6 -1 -1 -0.2 -0.88 -0.01 0.01
2 -0.286363636 -0.11818182 -0.572727273 -1 -1 -0.2363636 -0.8646281 0.000186 0.000331
3 -0.286032134 -0.11818573 -0.572064267 -1 -1 -0.2363715 -0.8647803 1.1E-07 1.53E-11
4 -0.286032164 -0.1181856 -0.572064327 -1 -1 -0.2363712 -0.8647805 9.16E-16 1.62E-14
N x1 x2 x3 x4 x1,i+1 x2,i+1 x3,i+1 x4,i+1 ep1 ep2 ep3 ep4
0 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.87500 5.00000
1 0.00000 1.00000 0.87500 5.00000 0.97500 1.97917 3.50000 4.68750 #DIV/0! 100.00000 100.00000 100.00000
2 0.97500 1.97917 3.50000 4.68750 1.24167 2.20208 3.34427 3.92431 100.00000 49.47368 75.00000 6.66667
3 1.24167 2.20208 3.34427 3.92431 1.01330 2.00448 2.95720 3.86866 21.47651 10.12299 4.65660 19.44789
4 1.01330 2.00448 2.95720 3.86866 0.96428 1.96876 2.93323 4.00417 22.53709 9.85781 13.08891 1.43828
5 0.96428 1.96876 2.93323 4.00417 0.99373 1.99552 3.00264 4.02229 5.08381 1.81451 0.81736 3.38411
6 0.99373 1.99552 3.00264 4.02229 1.00588 2.00520 3.01137 4.00135 2.96367 1.34094 2.31180 0.45049
7 1.00588 2.00520 3.01137 4.00135 1.00150 2.00114 3.00059 3.99626 1.20842 0.48278 0.28969 0.52326
8 1.00150 2.00114 3.00059 3.99626 0.99914 1.99922 2.99808 3.99946 0.43723 0.20296 0.35920 0.12745
9 0.99914 1.99922 2.99808 3.99946 0.99966 1.99973 2.99974 4.00059 0.23640 0.09581 0.08362 0.08009
10 0.99966 1.99973 2.99974 4.00059 1.00012 2.00011 3.00030 4.00014 0.05225 0.02549 0.05525 0.02826
11 1.00012 2.00011 3.00030 4.00014 1.00007 2.00005 3.00007 3.99991 0.04556 0.01888 0.01879 0.01121
12 1.00007 2.00005 3.00007 3.99991 0.99999 1.99999 2.99995 3.99997 0.00524 0.00283 0.00780 0.00582
13 0.99999 1.99999 2.99995 3.99997 0.99999 1.99999 2.99998 4.00001 0.00820 0.00345 0.00390 0.00143
14 0.99999 1.99999 2.99998 4.00001 1.00000 2.00000 3.00001 4.00001 0.00019 0.00019 0.00101 0.00112
15 1.00000 2.00000 3.00001 4.00001 1.00000 2.00000 3.00000 4.00000 0.00142 0.00061 0.00075 0.00015
16 1.00000 2.00000 3.00000 4.00000 1.00000 2.00000 3.00000 4.00000 0.00009 0.00002 0.00011 0.00020
17 1.00000 2.00000 3.00000 4.00000 1.00000 2.00000 3.00000 4.00000 0.00024 0.00010 0.00014 0.00001
SOLUCIN
;
ITERACIN X Y ex ey
1 1 1.4
2 0.993310962 1.42 0.673408 1.17239769
3 1.0011292 1.41 0.780942 0.19755824
4 0.999812207 1.41 0.131724 0.03286522
5 1.00003131 1.41 0.02191 0.00547923
6 0.999994782 1.41 0.003653 0.00091316
7 1.00000087 1.41 0.000609 0.00015219
8 0.999999855 1.41 0.000101 2.5366E-05
9 1.000000024 1.41 1.69E-05 4.2276E-06