/* 
************************************************************************
*  rungen.c: 4th order Runge-Kutta solution                            *
*  								       *
************************************************************************
*/
       
#include <stdio.h>
#include <math.h>

#define N 2                                   /* number of equations */
#define MIN 0.0                               /* minimum x */
#define MAX 10.0                              /* maximum x */
 
main()
{
   void rungen(double x, double y[], double dx);
   double f(double x, double y[], int i);
   
   double x, y[N], dx, h, yreal, yerror;
   int j;
   
   FILE *output;                              /* save data in rk4.dat */
   output = fopen("rungen.dat","w");

   printf("Input: dx\n");
   scanf("%lf", &dx);
   printf("dx=%g\n", dx);
   
   x = MIN;
   y[0] = 0.0;                                /* initial position  */
   y[1] = 1.0;                                /* initial velocity  */
   
   fprintf(output, "%f\t%f\n", x, y[0]);

   while(x <= MAX)
   {
      rungen(x, y, dx);
      x += dx;    
      yreal=sin(x);
      yerror=y[0]-yreal;      
      fprintf(output, "%f\t%f\t%f\t%e\n", x, y[0], yreal, yerror);
   }
   printf("data stored in rungen.dat\n");
   fclose(output);
}
/*-----------------------end of main program--------------------------*/

/* Runge-Kutta subroutine */
void rungen(double x, double y[], double step)
{
   double f(double x, double y[], int i);
   double h=step/2.0,                         /* the midpoint */
          t1[N], t2[N], t3[N],                /* temporary storage */
          k1[N], k2[N], k3[N],k4[N];          /* for Runge-Kutta  */
   int i;
 
   for (i=0; i<N; i++) t1[i] = y[i]+0.5*(k1[i]=step*f(x, y, i));
   for (i=0; i<N; i++) t2[i] = y[i]+0.5*(k2[i]=step*f(x+h, t1, i));
   for (i=0; i<N; i++) t3[i] = y[i]+    (k3[i]=step*f(x+h, t2, i));
   for (i=0; i<N; i++) k4[i] =                 step*f(x + step, t3, i);

   for (i=0; i<N; i++) y[i] += (k1[i]+2*k2[i]+2*k3[i]+k4[i])/6.0;
}
/*--------------------------------------------------------------------*/

/* definition of equations - this is the harmonic oscillator */
double  f(double x, double y[], int i)
{
   if (i == 0) return(y[1]);               /* RHS of first equation */
   if (i == 1) return(-y[0]);              /* RHS of second equation */
}