Method to find solution of ordinary differential equations

ODE-Adams-Bashforth-Moulton.py

import math, sys 
import numpy as np
#Adams-Bashforth technique: Predictor
#Adams-Moulton technique: Corrector

def PredictorCorrector(f, y0, T, n):
    #Use RungeKutta4
    """Solve y'=f(t,y), y(0)=y0, with n steps until t=T."""
    t = np.zeros(n+2)
    y = np.zeros(n+2)
    y[0] = y0
    t[0] = 0
    dt = T/float(n)
    print("\nH value:",dt)
    y, t = RungeKutta4(f, y0, T, n)
    
    f0 = f(y[0],t[0])
    f1 = f(y[1],t[1])
    f2 = f(y[2],t[2])
    f3 = f(y[3],t[3])
    #f4 = f(y[4],t[4])
    
    for k in range(n-1,0,-1):
        #Predictor: The fourth-order Adams-Bashforth technique, an explicit four-step method, is defined as:
        y[k+1] = y[k] + (dt/24) *(55*f3 - 59*f2 + 37*f1 - 9*f0)
        f4_AB = f(y[k+1],t[k+1])
        
        #Corrector: The fourth-order Adams-Moulton technique, an implicit three-step method, is defined as:              
        y[k+1] = y[k] + (dt/24) *(9*f(y[k+1],t[k+1]) + 19*f3 - 5*f2 + f1)
        y[k+1] = y[k] + (dt/24) *(9*f(y[k+1],t[k+1]) + 19*f3 - 5*f2 + f1)
    return y, t