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¿Qué es un método numérico? - page 76 / 82

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yi+1 = yi + (xi,yi,h)h___ (5.8)

(xi,yi,h) = a1k1 + a2k2 + ... + ankn___ (5.9)

donde: ai , constantes y

k1 = f(xi,yi)

k2 = f(xi + p1h, yi + q11k1h)

k3 = f(xi + p2h, yi + q21k1h + q22k2h)

...

kn  = f(xi + pn-1h, yi + qn-1,1k1h + qn-1,2k2h + ... + qn-1,n-1kn-1h)

Método de Runge Kutta de primer orden = Método de Euler:

n = 1 ;(xi,yi,h) = a1k1 ;a1 = 1 ;k1 = f(xi,yi)

yi+1 = yi + f(xi,yi)h

Métodos de Runge Kutta de segundo orden:

n = 2 ;(xi,yi,h) = a1k1 + a2k2 ;yi+1 = yi + (a1k1 + a2k2)h

k1 = f(xi,yi)

k2 = f(xi + p1h, yi + q11k1h)

yi+1 = yi + f(xi,yi)h+ f'(xi,yi)h2/2!

f'(xi,yi) = f/x + (f/y)dy/dx

yi+1 = yi + f(xi,yi)h+ [f/x + (f/y)dy/dx]h2/2!__ (5.10)

Considerando que:  g(x+r, y+s) = g(x,y) + rg/x + sg/y

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