python-pro

#Numerical Integration
import math

def dydx(x, y):
    return (y**2-2*x)/(y**2+x)
 
# Finds value of y for a given x using step size h
# and initial value y0 at x0.
def rungeKutta(x0, y0, x, h):
    # Count number of iterations using step size or
    # step height h
    n = (int)((x - x0)/h)
    # Iterate for number of iterations
    y = y0
    for i in range(1, n + 1):
        print("i  : ",i,"\nx0 : ",x0)
        "Apply Runge Kutta Formulas to find next value of y"
        k1 = h * dydx(x0, y)
        k2 = h * dydx(x0 + 0.5 * h, y + 0.5 * k1)
        k3 = h * dydx(x0 + 0.5 * h, y + 0.5 * k2)
        k4 = h * dydx(x0 + h, y + k3)
        print("k1 : ", k1)
        print("k2 : ", k2)
        print("k3 : ", k3)
        print("k4 : ", k4)
        print("\nk : ",(1.0 / 6.0)*(k1 + 2 * k2 + 2 * k3 + k4))
        # Update next value of y
        y = y + (1.0 / 6.0)*(k1 + 2 * k2 + 2 * k3 + k4)
        print("y",i," is ",y,sep="")
        print()
 
        # Update next value of x
        x0 = x0 + h
    return y
 
x0 = 0
y = 1

x = 0.5
h = 0.1

print('The value of y at x is:', rungeKutta(x0, y, x, h))
#hacktoberfest-2021