rungekutta.py

from __future__ import division

## Equations:
# x(t+h) = x(t) + 1/2 (F1 + F2)
# F1 = h*f(t,x)
# F2 = h*f(t+h, x+h*f(t,x))

def rungekutta(f, a, b, x0, iterations):
    h = (b - a) / iterations
    x = x0
    result = [x]
    for i in range(iterations):
        s = a + h*i
        F1 = h*f(s, x)
        F2 = h*f(s+h, x+F1)
        x = x + .5*(F1 + F2)
        result.append(x)
    return result