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'''
Solving initial value problem using 4th order Runge-Kutta method.
derivative depends on the value of the function.
f(x,y) = 1 + y**2
'''
from pylab import *
def f1(x,y):
return 1 + y**2
def f2(x,y):
return (y-x)/(y+x)
def rk4(x, y, fxy, h): # x, y , f(x,y)
k1 = h * fxy(x, y)
k2 = h * fxy(x + h/2.0, y+k1/2)
k3 = h * fxy(x + h/2.0, y+k2/2)
k4 = h * fxy(x + h, y+k3)
ny = y + ( k1/6 + k2/3 + k3/3 + k4/6 )
#print x,y,k1,k2,k3,k4, ny
return ny
h = 0.2 # stepsize
x = 0.0 # initail values
y = 0.0
print rk4(x,y,f1,h)
h = 1 # stepsize
x = 0.0 # initail values
y = 1.0
print rk4(x,y,f2,h)
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