Eulermethod.cpp

/*Consider below differential equation
            dy/dx = (x + y + xy)
    with initial condition y(0) = 1 
    and step size h = 0.025.
    Find y(0.1).
   
    Solution:
    f(x, y) = (x + y + xy)
    x0 = 0, y0 = 1, h = 0.025
    Now we can calculate y1 using Euler formula
    y1 = y0 + h * f(x0, y0)
    y1 = 1 + 0.025 *(0 + 1 + 0 * 1)
    y1 = 1.025
    y(0.025) = 1.025.
    Similarly we can calculate y(0.050), y(0.075), ....y(0.1).
    y(0.1) = 1.11167
    */
   /* C++ Program to find approximation
of a ordinary differential equation
using euler method.*/
#include <iostream>
using namespace std;

// Consider a differential equation
// dy/dx=(x + y + xy)
float func(float x, float y)
{
	return (x + y + x * y);
}

// Function for Euler formula
void euler(float x0, float y, float h, float x)
{
	float temp = -0;

	// Iterating till the point at which we
	// need approximation
	while (x0 < x) {
		temp = y;
		y = y + h * func(x0, y);
		x0 = x0 + h;
	}

	// Printing approximation
	cout << "Approximate solution at x = "
		<< x << " is " << y << endl;
}

int main()
{
	// Initial Values
	float x0 = 0;
	float y0 = 1;
	float h = 0.025;

	// Value of x at which we need approximation
	float x = 0.1;

	euler(x0, y0, h, x);
	return 0;
}