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¿Qué es un método numérico? - page 80 / 82

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k3 = f(xi + h/2, yi + k2h/2)

k4 = f(xi + h, yi + k3h)

Ejemplo.  Resolver la ecuación diferencial ordinaria asociada al problema del paracaidista, usando el método clasico de Runge Kutta de cuarto orden.

d/dt = g - k/m ;(0) = 0 ;h = 2 ;

k1 = f(ti,i) = g - (k/m)i= 9.81 - 0.18355360 i

k2 = f(ti + h/2, i + k1h/2) = f(ti + 1, i + k1)

= g - (k/m)[i + 9.81 - 0.18355360 i]

= 9.81 - 0.18355360[i + 9.81 - 0.18355360 i]

= 9.81 - 0.18355360i - 1.80066082 + 0.03435661 i

= 8.00933918 - 0.14919699 i

k3 = f(ti + h/2, i + k2h/2) = f(ti + 1, i + k2)

= g - (k/m)[i + 8.00933918 - 0.14919699 i]

= 9.81 - 0.18355360[i + 8.00933918 - 0.14919699 i]

= 9.81 - 0.18355360i - 1.47014305 + 0.02738565 i

= 8.33985695 - 0.15616795 i

k4 = f(ti + h, i + k3h) = f(ti + 2, i + 2k3)

= g - (k/m)[i + 2(8.33985695 - 0.15616795 i)]

= 9.81 - 0.18355360[i + 16.6797139 - 0.31233590 i]

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