Differential Equations by Runge-Kutta Method

AIM: Write a Python program to find numerical solution of ordinary differential equations by Runge-Kutta method.

Source Code:

# RK-4 method python program

# function to be solved
def f(x,y):
  return x+y

# RK-4 method
def rk4(x0,y0,xn,n):
 
# Calculating step size
  h = (xn-x0)/n
 
  print("--------SOLUTION--------")
  print("-------------------------")
  print("x0\ty0\tyn")
  print("-------------------------")
  for i in range(n):
    k1 = h * (f(x0, y0))
    k2 = h * (f((x0+h/2), (y0+k1/2)))
    k3 = h * (f((x0+h/2), (y0+k2/2)))
    k4 = h * (f((x0+h), (y0+k3)))
    k = (k1+2*k2+2*k3+k4)/6
    yn = y0 + k
    print("%.4f\t%.4f\t%.4f"% (x0,y0,yn) )
    print("-------------------------")
    y0 = yn
    x0 = x0+h
 
  print("At x=%.4f, y=%.4f" %(xn,yn))

print("Enter initial conditions:")
x0 = float(input("x0 = "))
y0 = float(input("y0 = "))

print("Enter calculation point: ")
xn = float(input("xn = "))

print("Enter number of steps:")
step = int(input("Number of steps = "))

rk4(x0,y0,xn,step)

Output:

Enter initial conditions:
x0 = 0
y0 = 1
Enter calculation point: 
xn = 1
Enter number of steps:
Number of steps = 3   
--------SOLUTION-------- 
-------------------------
x0      y0      yn       
-------------------------
0.0000  1.0000  1.4578
-------------------------
0.3333  1.4578  2.2286
-------------------------
0.6667  2.2286  3.4361
-------------------------
At x=1.0000, y=3.4361