Ordinary Differential Equation Using Fourth Order Runge Kutta (RK) Method Using C


This program is implementation of Runge Kutta Fourth Order method for solving ordinary differential equation using C programming language with output.

Output of this is program is solution for dy/dx = (y2 - x2)/(y2+x2) with initial condition y = 1 for x = 0 i.e. y(0) = 1 and we are trying to evaluate this differential equation at y = 0.4 in two steps i.e. n = 2. ( Here y = 0.4 i.e. y(0.4) = ? is our calculation point)

C Program for RK-4 Method


#include<stdio.h>
#include<conio.h>

#define f(x,y) (y*y-x*x)/(y*y+x*x)

int main()
{
 float x0, y0, xn, h, yn, k1, k2, k3, k4, k;
 int i, n;
 clrscr();
 printf("Enter Initial Condition\n");
 printf("x0 = ");
 scanf("%f", &x0);
 printf("y0 = ");
 scanf("%f", &y0);
 printf("Enter calculation point xn = ");
 scanf("%f", &xn);
 printf("Enter number of steps: ");
 scanf("%d", &n);

 /* Calculating step size (h) */
 h = (xn-x0)/n;

 /* Runge Kutta Method */
 printf("\nx0\ty0\tyn\n");
 for(i=0; i < n; i++)
 {
  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;
  printf("%0.4f\t%0.4f\t%0.4f\n",x0,y0,yn);
  x0 = x0+h;
  y0 = yn;
 }

 /* Displaying result */
 printf("\nValue of y at x = %0.2f is %0.3f",xn, yn);

 getch();
 return 0;
}

RK Method C Program Output

Enter Initial Condition
x0 = 0
y0 = 1
Enter calculation point xn = 0.4
Enter number of steps: 2

x0      y0      yn
0.0000  1.0000  1.1960
0.2000  1.1960  1.3753

Value of y at x = 0.40 is 1.375

Recommended Readings

  1. Ordinary Differential Equation Using Euler's Method Algorithm
  2. Ordinary Differential Equation Using Euler's Method Pseudocode
  3. Ordinary Differential Equation Using Euler's Method Using C Programming
  4. Ordinary Differential Equation Using Euler's Method Using C++ Programming
  5. Ordinary Differential Equation Using Fourth Order Runge Kutta (RK) Method Algorithm
  6. Ordinary Differential Equation Using Fourth Order Runge Kutta (RK) Method Pseudocode
  7. Ordinary Differential Equation Using Fourth Order Runge Kutta (RK) Method Using C
  8. Runge Kutta (RK) Fourth Order Using C++ with Output