/* 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; and CC Bordeianu, Univ Bucharest, 2007.
   Support by National Science Foundation                              
*/
// rk4.java: 4th order Runge-Kutta ODE Solver for arbitrary y(t)

import java.io.*; 

public class RK4  {
  
  public static void main(String[] argv) 
                         throws IOException, FileNotFoundException {
													 
    PrintWriter w =                                 // Output to file
              new PrintWriter(new FileOutputStream("rk4.dat"), true);
							
    double h, t;                    
		double ydumb[] = new double[2]; 
    double y[] = new double[2];     
		double fReturn[] = new double[2];
    double k1[] = new double[2];    
		double k2[] = new double[2];  
    double k3[] = new double[2];    
		double k4[] = new double[2];    
    double a = 0. ;    double b = 10. ;                  // Endpoints
    int i, n = 100; 
		
    y[0] = 3. ;    y[1] = -5. ;                         // Initialize
    h = (b-a)/n;  
    t = a; 
    System.out.println("rk4_rhl t = "    // Printout for initial step
                          + t + " , x = " + y[0] + ", v = " + y[1]);
    w.println(t + " " + y[0] + " " + y[1]);  // Output answer to file
		                                               //  Loop over time
    while (t < b)  {   
      if ( (t + h) > b ) h = b - t;                      // Last step
      f(t, y, fReturn);          // Evaluate RHS's, return in fReturn
      k1[0] = h*fReturn[0];                // Compute function values
      k1[1] = h*fReturn[1]; 
      for ( i=0; i <= 1; i++ )  ydumb[i] = y[i] + k1[i]/2; 
      f(t + h/2, ydumb, fReturn); 
      k2[0] = h*fReturn[0]; 
      k2[1] = h*fReturn[1]; 
      for ( i=0; i <= 1; i++ )  ydumb[i] = y[i] + k2[i]/2; 
      f(t + h/2, ydumb, fReturn); 
      k3[0] = h*fReturn[0];  
      k3[1] = h*fReturn[1]; 
      for ( i=0; i <= 1; i++ )  ydumb[i] = y[i] + k3[i]; 
      f(t + h, ydumb, fReturn); 
      k4[0] = h*fReturn[0];   
      k4[1] = h*fReturn[1];   
      for (i=0;i <= 1; i++)y[i]=y[i]+(k1[i]+2*(k2[i]+k3[i])+k4[i])/6;
      t = t + h;    
      System.out.println("in Rk4, t = "                  // Printout
                           + t + " , x = " + y[0] + ", v = " + y[1]);
      w.println(t + " " + y[0] + " " + y[1]);          // File output
    }                                               // End while loop
  } 
  
                                      // FUNCTION of your choice here
  public static void f( double t, double y[], double fReturn[] )  
    { fReturn[0] = y[1];                                // RHS 1st eq
      fReturn[1] = -100*y[0]-2*y[1] + 10*Math.sin(3*t); }  // RHS 2nd
}