eulers_method.py

Created on September 22, 2021

942 Bytes

In this Python program x0 and y0 represent the initial condition. xn is the calculation point on which the value of yn corresponding to xn is to be calculated using Euler’s method. step represents number of finite step before reaching to xn.

from math import *

# Euler method python program

# function to be solved
def f(x,y):
    return 18*x*sin(0.79*x)

# Euler method
def euler(x0,y0,xn,n):
    
    # Calculating step size
    h = (xn-x0)/n
    
    print('\n-----------SOLUTION-----------')
    print('------------------------------')    
    print('x0\ty0\tslope\tyn')
    print('------------------------------')
    for i in range(n):
        slope = f(x0, y0)
        yn = y0 + h * slope
        print('%.3f\t%.3f\t%0.3f\t%.3f'% (x0,y0,slope,yn) )
        print('------------------------------')
        y0 = yn
        x0 = x0+h
    
    print('\nAt x=%.4f, y=%.4f' %(xn,yn))

# Inputs
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 = '))

# Euler method call
euler(x0,y0,xn,step)