Single Time Step for Runge Kutta 4th Order

rk4.py

#Runge-Kutta Method Single Time Step
def rk4(func,t,a,b,c,dt):
    """
    Peforms a single time step of the Runge-Kutta 4th Order Method.
    The below function finds the ki value for [dx,dy,dz] and return the value to move Yn+1
    func is an input of functions, for the Lorenz system this is [dx,dy,dz]
    
    Recall Rk4 Equations :
    k1 = h*f(xn,yn)
    k2 = h*f(xn+h/2,yn+k1/2)
    k3 = h*f(xn+h/2,yn+k2/2)
    k4 = h*f(xn,yn+k3)
    Where f is a function [dx,dy,dz]
    Yn+1 = Yn + 1/6*(k1+k2+k3+k4)
    """
    
    k1,k2,k3,k4 = [],[],[],[]
    for f in func:
        k1.append(dt*f(t,a,b,c))
    for f in func:
        k2.append(dt*f(t+dt/2,a+k1[0]/2,b+k1[1]/2,c+k1[2]/2))
    for f in func:
        k3.append( dt*f(t+dt/2,a+k2[0]/2,b+k2[1]/2,c+k2[2]/2))
    for f in func:
        k4.append( dt*f(t+dt/2,a+k3[0],b+k3[1],c+k3[1]))
    k1,k2,k3,k4 = np.array(k1),np.array(k2),np.array(k3),np.array(k4)
    return (1/6)*(k1+k2+k3+k4)