#!/usr/bin/python3
# 4th order Runge-Kutta method

import numpy as np

def rk4(f, a, b, x0, N):
    h = (b - a) / N
    x = x0
    tpoints = np.linspace(a, b, N+1)
    xpoints = []
    
    for t in tpoints:
        xpoints += [x]
        k1 = h * f(x, t)
        k2 = h * f(x + k1/2, t + h/2)
        k3 = h * f(x + k2/2, t + h/2)
        k4 = h * f(x + k3, t + h)
        x = x + (k1 + 2*k2 + 2*k3 + k4)/6
        
    return tpoints, np.array(xpoints)