ecuaciones metodo euler
DESCRIPTION
metodo de euler ecuaciones diferencialesTRANSCRIPT
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Hallar los valores aproximados de la solucion del problema dado con valorinicial, en t = t0 + 0.1, t0 + 0.2, t0 + 0.3 y t0 + 0.4:
a) Aplicar el metodo de Euler con h = 0.1
b) Aplicar el metodo de Euler con h = 0.05
c) Aplicar el metodo de Euler con h = 0.025
1. y = ex2, x(0) = 1
a) Aplicando el metodo de Euler: yn+1 = yn + hf(tn, yn) con h = 0.1Sea t1 = 1 + 0.1Para t1 = 1.1y1 = 3 + (0.1)f(1.1 , 3)y1 = 3 + (0.1)(2.0248)y1 = 3.2024
Para t2 = 1.2y2 = 3.2024 + (0.1)f(1.2 , 3.2024)y2 = 3.2024 + (0.1)(2.0982)y2 = 3.4122
Para t3 = 1.3y3 = 3.4122 + (0.1)f(1.3 , 3.4122)y3 = 3.4122 + (0.1)(2.1707)y3 = 3.6292
Para t4 = 1.4y4 = 3.6292 + (0.1)f(1.2 , 3.2024)y4 = 3.6292 + (0.1)(2.0982)y4 = 3.4122
b) Aplicando el metodo de Euler: yn+1 = yn + hf(tn, yn) con h = 0.05
Para t1 = 1.1y1 = 3 + (0.05)f(1.1 , 3)y1 = 3 + (0.05)(2.0248)y1 = 3.1012
Para t2 = 1.15y2 = 3.1012 + (0.05)f(1.15 , 3.1012)
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y2 = 3.1012 + (0.05)(2.0618)y2 = 3.2042
Para t3 = 1.2y3 = 3.2042 + (0.05)f(1.2 , 3.2042)y3 = 3.2042 + (0.05)(2.0986)y3 = 3.3091
Para t4 = 1.25y4 = 3.3091 + (0.05)f(1.25 , 3.3091)y4 = 3.3091 + (0.05)(2.1352)y4 = 3.4158
Para t5 = 1.3y5 = 3.4158 + (0.05)f(1.3 , 3.4158)y5 = 3.4158 + (0.05)(2.1716)y5 = 3.5243
Para t6 = 1.35y6 = 3.5243 + (0.05)f(1.35 , 3.5243)y6 = 3.5243 + (0.05)(2.2077)y6 = 3.6346
Para t7 = 1.4y7 = 3.6346 + (0.05)f(1.4 , 3.6346)y7 = 3.6346 + (0.05)(2.2438)y7 = 3.7467
Para t8 = 1.45y8 = 3 + (0.05)f(1.45 , 3.7467)y8 = 3 + (0.05)(2.2796)y8 = 3.860
c) De manera similar se obtienen los resultados de h = 0.025 y se muestranen la siguiente tabla:
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n tn yn f(tn, yn) Aproximacion1 1.025 3 2.1246 3.05032 1.05 3.0503 2.0310 3.10103 1.075 3.1010 2.0496 3.15234 1.1 3.1523 2.0681 3.20405 1.125 3.2040 2.0866 3.25626 1.15 3.2562 2.1050 3.30887 1.175 3.3088 2.1233 3.36198 1.2 3.3619 2.1417 3.41549 1.225 3.4154 2.1599 3.469410 1.25 3.4694 2.1781 3.523911 1.275 3.5239 2.1963 3.578812 1.3 3.5788 2.2144 3.634113 1.325 3.6368 2.2325 3.689914 1.35 3.6899 2.2505 3.746215 1.375 3.7462 2.2685 3.802916 1.4 3.8029 2.2864 3.8601
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