EULER’S METHOD

        Euler’s method is one of the methods to solve the ordinary differential equation for first order equation.

The formula for Eulers method is given by:

          y_n+1=y_n+ h * f((x_n, y_n)

where,

          i= 1,2,3,4,……….

          h = step size

Source code for Euler’s method

#include<iostream>

#include<cmath>

using namespace std;

int main(){

    float x, X, y, n, h, m;

    cout<<"Enter initial value of x & y, final value of x and number of steps : "<<endl;

    cin>>x>>y>>X>>n;

    h = ( X - x ) / n;

    do{

        cout<<"f("<<x<<") = "<<y<<endl;

        m = ( y - x ) / ( y + x );

        y += m * h;

        x = x + h;

    }while(x<=X);

    return 0;

}

Source code for Modified Euler’s method

#include<iostream>

#include<cmath>

using namespace std;

int main(){

    float x, X, y, y1, Y, h, m, M;

    cout<<"Enter initial value of x & y, final value of x and stepping value :\n";

    cin>>x>>y>>X>>h;

    do{

        cout<<"f("<<x<<") = "<<y<<endl;

        M = ( y - x ) / ( y + x );  m = M;

        x = x + h;

        Y = y;

        do{

            y1 = y;

            y = Y + m * h;

            cout<<"f("<<x<<") = "<<y<<endl;

            m = ( y - x ) / ( y + x );

            m = ( M + m ) / 2;

        }while((abs(y1-y))>0.00004);

    }while(x<X);

    return 0;

}