• Author / Uploaded
• savageorion5013

• Categories
• Algoritmos
• Resta
• Matemática aplicada
• Ciencias computacionales
• Conceptos matemáticos

Citation preview

PROBLEMA 01 h = 0.500000 Numero de intervalos = 9 ******* SOLUCION POR EL METODO DE EULER ******* N X Y 1 0.000000 1.000000 2 0.500000 5.250000 3 1.000000 5.875000 4 1.500000 5.125000 5 2.000000 4.500000 6 2.500000 4.750000 7 3.000000 5.875000 8 3.500000 7.125000 9 4.000000 7.000000

******* VALORES DE LA SOLUCION EXACTA ******* N X Y 1 0.000000 1.000000 2 0.500000 3.218750 3 1.000000 3.000000 4 1.500000 2.218750 5 2.000000 2.000000 6 2.500000 2.718750 7 3.000000 4.000000 8 3.500000 4.718750 9 4.000000 3.000000

Grafico Azul: Solución aproximada Rojo: Solución exacta

PROBLEMA 01 h = 0.500000 Numero de intervalos = 9 ******* SOLUCION POR EL METODO DE RUNGE KUTTA ******* N X Y 1 0.000000 1.000000 2 0.500000 3.222222 3 1.000000 3.006944 4 1.500000 2.229167 5 2.000000 2.013889 6 2.500000 2.736111 7 3.000000 4.020833 8 3.500000 4.743056 9 4.000000 3.027778

******* VALORES DE LA SOLUCION EXACTA ******* N X Y 1 0.000000 1.000000 2 0.500000 3.218750 3 1.000000 3.000000 4 1.500000 2.218750 5 2.000000 2.000000 6 2.500000 2.718750 7 3.000000 4.000000 8 3.500000 4.718750 9 4.000000 3.000000

Grafico Azul: Solución aproximada Rojo: Solución exacta

Solución a) PROBLEMA 02 h = 0.100000 Numero de intervalos = 11 ******* SOLUCION POR EL METODO DE EULER ******* N t T 1 0.000000 298.000000 2 0.100000 300.000000 3 0.200000 301.999000

4 0.300000 5 0.400000 6 0.500000 7 0.600000 8 0.700000 9 0.800000 10 0.900000 11 1.000000 Rpta T(1) = 317.715 °

303.995000 305.986000 307.970000 309.945000 311.909000 313.860000 315.796000 317.715000

Grafico Azul: Solución aproximada

Solución b) PROBLEMA 02 h = 0.200000 Numero de intervalos = 6 ******* SOLUCION POR EL METODO DE RUNGE KUTTA ******* N t T 1 0.000000 298.000000 2 0.200000 301.997333 3 0.400000 305.978667 4 0.600000 309.928000 5 0.800000 313.829333 6 1.000000 317.666667 Rpta T(1) = 317.666667 °

Grafico Azul: Solución aproximada

PROBLEMA 03 h = 0.500000 Numero de intervalos = 31 ******* SOLUCION POR EL METODO DE EULER ******* N t v 1 0.000000 0.000000 2 0.500000 4.900000 3 1.000000 9.350294 4 1.500000 13.392154 5 2.000000 17.063065 6 2.500000 20.397071 7 3.000000 23.425093 8 3.500000 26.175213 9 4.000000 28.672936 10 4.500000 30.941426 11 5.000000 33.001721 12 5.500000 34.872928

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

6.000000 6.500000 7.000000 7.500000 8.000000 8.500000 9.000000 9.500000 10.000000 10.500000 11.000000 11.500000 12.000000 12.500000 13.000000 13.500000 14.000000 14.500000 15.000000

36.572403 38.115905 39.517749 40.790936 41.947275 42.997488 43.951316 44.817605 45.604389 46.318964 46.967958 47.557389 48.092724 48.578928 49.020509 49.421564 49.785811 50.116629 50.417085

******* VALORES DE LA SOLUCION EXACTA ******* N t v 1 0.000000 0.000000 2 0.500000 4.681871 3 1.000000 8.953182 4 1.500000 12.849937 5 2.000000 16.404981 6 2.500000 19.648278 7 3.000000 22.607167 8 3.500000 25.306587 9 4.000000 27.769291 10 4.500000 30.016038 11 5.000000 32.065765 12 5.500000 33.935749 13 6.000000 35.641752 14 6.500000 37.198153 15 7.000000 38.618071 16 7.500000 39.913475 17 8.000000 41.095283 18 8.500000 42.173457 19 9.000000 43.157085 20 9.500000 44.054457 21 10.000000 44.873138 22 10.500000 45.620027 23 11.000000 46.301421 24 11.500000 46.923062 25 12.000000 47.490191 26 12.500000 48.007588 27 13.000000 48.479613 28 13.500000 48.910246 29 14.000000 49.303116

30 31

14.500000 15.000000

49.661535 49.988524

Rpta: Euler, velocidad al segundo 15 = 50.417085 m/s Solución exacta, velocidad al segundo 15 = 49.988524 m/s

Grafico Azul: Solución aproximada Rojo: Solución exacta

Ingrese h = 0.1 h= 0.1000 PROBLEMA 04 h = 0.100000 Numero de intervalos = 151 ******* SOLUCION POR EL METODO DE RUNGE KUTTA ******* N t v 1 0.000000 0.000000 151 15.000000 35.575989

Rpta: con h = 0.1 velocidad al segundo 15 es 35.575989m/s Grafico

Ingrese h = 0.2 h= 0.2000 PROBLEMA 04 h = 0.200000 Numero de intervalos = 76 ******* SOLUCION POR EL METODO DE RUNGE KUTTA *******

N t v 1 0.000000 0.000000 76 15.000000 35.575939 Rpta: con h = 0.1 velocidad al segundo 15 es 35.575939m/s Grafico

Solución a) PROBLEMA 05 h = 0.100000 Numero de intervalos = 11 ******* SOLUCION POR EL METODO DE EULER ******* N t v 1 0.000000 8.000000 2 0.100000 6.903636 3 0.200000 5.836981 4 0.300000 4.795035

5 0.400000 3.773231 6 0.500000 2.767345 7 0.600000 1.773421 8 0.700000 0.787703 9 0.800000 -0.193425 10 0.900000 -1.173493 11 1.000000 -2.155997 Rpta: con h = 0.1 velocidad al segundo 15 es 2.155997m/s (de caida) Gráfico

Solución b) Ingrese h = 0.2 h= 0.2000 PROBLEMA 05 h = 0.200000 Numero de intervalos = 6 ******* SOLUCION POR EL METODO DE RUNGE KUTTA ******* N t v 1 0.000000 8.000000 2 0.200000 5.865233 3 0.400000 3.819340 4 0.600000 1.829341 5 0.800000 -0.134423 6 1.000000 -2.100104 Rpta: con h = 0.1 velocidad al segundo 15 es 2.100104m/s (de caida)

Gráfico

t= 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

x= 2.0000 2.1249 2.2597 2.4048 2.5603

1.0000 0.9820 0.9681 0.9584 0.9531

2.7264 2.9030 3.0897 3.2861 3.4911 3.7033

0.9524 0.9566 0.9661 0.9813 1.0028 1.0312

Grafico X: azul Y: verde

Solución a) PROBLEMA 07-a Ode45: y1(0)=y2(0)=1, u = 1, tinicial=0 y tfinal=20

t= 0 0.0502 0.1005 0.1507 0.2010 0.3377 0.4744 0.6111 0.7478 0.8786 1.0094 1.1403 1.2711 1.4379 1.6048 1.7716 1.9384 2.0240 2.1095 2.1951 2.2806 2.3662 2.4517 2.5372 2.6228 2.7102 2.7976 2.8850 2.9724 3.0598 3.1472 3.2346 3.3220 3.3961 3.4703 3.5444 3.6186 3.6807 3.7429 3.8050 3.8672 3.9455 4.0239 4.1022 4.1806 4.2944 4.4082 4.5221 4.6359

4.8119 4.9879 5.1639 5.3399 5.4412 5.5425 5.6438 5.7450 5.8463 5.9476 6.0489 6.1502 6.2374 6.3247 6.4119 6.4991 6.5694 6.6396 6.7098 6.7801 6.8436 6.9071 6.9706 7.0341 7.1000 7.1660 7.2320 7.2980 7.3904 7.4828 7.5752 7.6676 7.8219 7.9761 8.1304 8.2846 8.3959 8.5071 8.6184 8.7296 8.8409 8.9521 9.0634 9.1747 9.2773 9.3799 9.4826 9.5852 9.6685 9.7517 9.8349 9.9182

9.9719 10.0256 10.0793 10.1330 10.1867 10.2404 10.2941 10.3478 10.4141 10.4804 10.5467 10.6130 10.7024 10.7917 10.8811 10.9704 11.1161 11.2619 11.4076 11.5534 11.6697 11.7860 11.9022 12.0185 12.1348 12.2511 12.3674 12.4837 12.5847 12.6858 12.7869 12.8879 12.9709 13.0538 13.1367 13.2197 13.2884 13.3571 13.4258 13.4945 13.5507 13.6068 13.6630 13.7192 13.7875 13.8559 13.9242 13.9926 14.0864 14.1802 14.2740 14.3678

14.5291 14.6905 14.8518 15.0131 15.1223 15.2315 15.3407 15.4499 15.5592 15.6684 15.7776 15.8868 15.9922 16.0976 16.2029 16.3083 16.3951 16.4819 16.5688 16.6556 16.7120 16.7684 16.8247 16.8811 16.9375 16.9939 17.0503 17.1066 17.1786 17.2506 17.3226 17.3946 17.4952 17.5957 17.6963 17.7969 17.9897 18.1826 18.3754 18.5682 18.6680 18.7678 18.8676 18.9674 19.0672 19.1670 19.2668 19.3666 19.4403 19.5139 19.5876 19.6612

19.7348 19.8085 19.8821 19.9557 19.9668 19.9779 19.9889 20.0000

x= 1.0000 1.0489 1.0949 1.1378 1.1771 1.2650 1.3235 1.3530 1.3551 1.3344 1.2940 1.2357 1.1608 1.0418 0.8955 0.7188 0.5063 0.3812 0.2436 0.0927 -0.0721 -0.2510 -0.4429 -0.6448 -0.8522 -1.0627 -1.2624 -1.4427 -1.5966 -1.7198 -1.8118 -1.8750 -1.9128 -1.9282 -1.9312 -1.9239 -1.9084 -1.8901 -1.8678 -1.8420

1.0000 0.9461 0.8854 0.8187 0.7472 0.5370 0.3200 0.1116 -0.0772 -0.2364 -0.3792 -0.5101 -0.6343 -0.7928 -0.9637 -1.1602 -1.3948 -1.5331 -1.6839 -1.8448 -2.0102 -2.1705 -2.3088 -2.4035 -2.4302 -2.3624 -2.1908 -1.9255 -1.5921 -1.2316 -0.8816 -0.5668 -0.3019 -0.1182 0.0333 0.1570 0.2579 0.3283 0.3886 0.4409

-1.8131 -1.7729 -1.7289 -1.6814 -1.6306 -1.5510 -1.4647 -1.3710 -1.2693 -1.0938 -0.8906 -0.6513 -0.3654 -0.1751 0.0369 0.2708 0.5244 0.7922 1.0610 1.3150 1.5391 1.6976 1.8206 1.9090 1.9657 1.9922 2.0049 2.0061 1.9982 1.9847 1.9661 1.9434 1.9171 1.8867 1.8534 1.8176 1.7795 1.7225 1.6616 1.5967 1.5277 1.4028 1.2641 1.1087 0.9326 0.7898 0.6309 0.4529 0.2526 0.0275 -0.2246 -0.5015

0.4870 0.5385 0.5847 0.6277 0.6690 0.7284 0.7900 0.8568 0.9315 1.0695 1.2478 1.4808 1.7801 1.9833 2.2008 2.4131 2.5852 2.6686 2.6112 2.3896 2.0164 1.6192 1.2069 0.8190 0.4879 0.2718 0.0934 -0.0518 -0.1688 -0.2552 -0.3269 -0.3870 -0.4381 -0.4839 -0.5242 -0.5605 -0.5941 -0.6382 -0.6810 -0.7242 -0.7692 -0.8521 -0.9498 -1.0693 -1.2192 -1.3516 -1.5095 -1.6955 -1.9093 -2.1452 -2.3825 -2.5809

-0.7953 -1.0692 -1.3271 -1.5524 -1.7342 -1.8453 -1.9250 -1.9772 -2.0059 -2.0142 -2.0159 -2.0119 -2.0032 -1.9904 -1.9742 -1.9551 -1.9334 -1.9036 -1.8709 -1.8356 -1.7979 -1.7438 -1.6859 -1.6244 -1.5592 -1.4443 -1.3178 -1.1776 -1.0205 -0.8806 -0.7248 -0.5500 -0.3529 -0.1300 0.1220 0.4026 0.7053 0.9763 1.2377 1.4730 1.6697 1.7957 1.8896 1.9543 1.9933 2.0097 2.0145 2.0096 1.9971 1.9822 1.9639 1.9425

-2.6784 -2.6114 -2.3787 -2.0056 -1.5378 -1.1438 -0.7827 -0.4733 -0.2221 -0.0890 0.0243 0.1205 0.2019 0.2711 0.3302 0.3810 0.4252 0.4725 0.5139 0.5508 0.5846 0.6272 0.6681 0.7090 0.7512 0.8260 0.9125 1.0161 1.1435 1.2673 1.4162 1.5940 1.8028 2.0399 2.2915 2.5213 2.6657 2.6552 2.4853 2.1627 1.7225 1.3262 0.9477 0.6122 0.3340 0.1474 -0.0055 -0.1295 -0.2298 -0.2976 -0.3553 -0.4049

1.9185 1.8863 1.8512 1.8134 1.7733 1.7146 1.6518 1.5850 1.5140 1.3812 1.2330 1.0657 0.8744 0.7280 0.5649 0.3822 0.1770 -0.0530 -0.3088 -0.5869 -0.8778 -1.1559 -1.4110 -1.6267 -1.7939 -1.8929 -1.9595 -1.9989 -2.0161 -2.0176 -2.0130 -2.0032 -1.9891 -1.9713 -1.9505 -1.9269 -1.9010 -1.8649 -1.8259 -1.7842 -1.7399 -1.6742 -1.6038 -1.5287 -1.4485 -1.2789 -1.0837 -0.8548 -0.5808 -0.4165 -0.2337 -0.0304

-0.4479 -0.4936 -0.5338 -0.5701 -0.6037 -0.6475 -0.6904 -0.7341 -0.7800 -0.8682 -0.9739 -1.1055 -1.2730 -1.4126 -1.5782 -1.7716 -1.9905 -2.2263 -2.4522 -2.6233 -2.6778 -2.5519 -2.2558 -1.8353 -1.3456 -0.9480 -0.5996 -0.3130 -0.0875 0.0309 0.1304 0.2141 0.2845 0.3443 0.3954 0.4397 0.4786 0.5224 0.5614 0.5971 0.6309 0.6768 0.7230 0.7713 0.8236 0.9407 1.0915 1.2922 1.5621 1.7347 1.9306 2.1434

0.1942 0.4394 0.7002 0.9668 1.2256 1.4017 1.5584 1.6916 1.7992 1.8814 1.9405 1.9794 2.0011 2.0031 2.0047 2.0061 2.0072

2.3574 2.5472 2.6636 2.6582 2.4967 2.2713 1.9759 1.6373 1.2871 0.9551 0.6575 0.4027 0.1921 0.1640 0.1368 0.1105 0.0850

Gráfico

Solución b) PROBLEMA 07-b Ode23: y1(0)=y2(0)=1, u = 1000, tinicial=0 y tfinal=3000 Sistema inestable con el Dominio de t perteneciente [0,3000]

Gráfico

PROBLEMA 08 x= 0 1 2 3 4 5

6 7 8 9 10

y= 1.0e-004 * 0 -0.0020 -0.0078 -0.0169 -0.0289 -0.0434 -0.0600 -0.0783 -0.0978 -0.1181 -0.1389

0 -0.0040 -0.0075 -0.0106 -0.0133 -0.0156 -0.0175 -0.0190 -0.0200 -0.0206 -0.0208

Gráfico

Gráfico de la Solución exacta