C Program for Runge-Kutta-4 (RK-4) Method

#include <stdio.h>

#include <conio.h>

#include <math.h>

float f(float x,float y)

{

  return ((y*y-x*x)/(y*y+x*x));

  //y'=f(x,y)=equation

}

void main()

{

  float x0,y0,h,xn,yn;

  printf("Enter x0 and y0: ");

  scanf("%f%f",&x0,&y0); //y(x0)=y0

  printf("Enter xn: ");

  scanf("%f",&xn);

  printf("Enter interval(h): ");

  scanf("%f",&h);

  do

  {

    float m1=f(x0,y0);

    float m2=f(x0+h/2,y0+m1*h/2);

    float m3=f(x0+h/2,y0+m2*h/2);

    float m4=f(x0+h,y0+m3*h);

    float m=(m1+2*m2+2*m3+m4)/6;

    yn=y0+m*h;

    //for next iteration

    

    x0=x0+h;

    y0=yn;

  }while(x0<xn);

printf("\n\nHence, y(%0.1f)=%0.4f",xn,yn);

getch();

}

OUTPUT: