/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation
*/
//  rk4.c: 4th order Runge-Kutta solution for harmonic oscillator       
       
#include <stdio.h>
#define N 2                                    // number of equations
#define dist 0.1                                          // stepsize
#define MIN 0.0                                          // minimum x
#define MAX 10.0                                         // maximum x

main()  {
	
  double x, y[N];
  int j;
  void runge4(double x, double y[], double step);           // header
  double f(double x, double y[], int i);
	
  FILE *output;                               // save data in rk4.dat
  output= fopen("rk4.dat","w");
  y[0]= 1.0;                                      // initial position
  y[1]= 0.0;                                      // initial velocity
  fprintf(output, "%f\t%f\n", x, y[0]);
  
	for (x= MIN; x <=  MAX ; x += dist)  {
    runge4(x, y, dist);
    fprintf(output, "%f\t%f\n", x, y[0]);        // position vs. time
  }
  printf("data stored in rk4.dat\n");
  fclose(output);
}                                             // -end of main program

void runge4(double x, double y[], double step)  {    // rk subroutine
  double f(double x, double y[], int i);
  double h = step/2.0,                                // the midpoint
  t1[N], t2[N], t3[N], 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;
} 

double f(double x, double y[], int i) {               // RHS function                      
  if (i ==  0) return(y[1]);                 // RHS of first equation
  if (i ==  1) return(-y[0]);               // RHS of second equation
}