/* 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                              
*/
// rk2.java:  Runge-Kutta 2nd order  ODE solver

import java.io.*; 

public class Rk2  {
  
  public static void main(String[] argv) 
                          throws IOException, FileNotFoundException {
														
    PrintWriter w =                                    // Output file
              new PrintWriter(new FileOutputStream("rk2.dat"), true);
							
    double h, t, a = 0., b = 10. ;                       // Endpoints
    double y[] = new double[2], ydumb[] = new double[2]; 
    double fReturn[] = new double[2];  
    double k1[] = new double[2];  
		double k2[] = new double[2];  
    int i, n=100; 
		
    y[0] = 3. ;   y[1] = -5. ;                          // Initialize
    h = (b-a)/n;  
    t = a; 
    System.out.println("rk2  t="+t+" , x = " +y[0]+ ", v = " + y[1]);  
    w.println(t + " " + y[0] + " " + y[1]);         // Output to file
		                                               // Loop over time
    while (t < b)  {   
      if ( (t + h) > b ) h = b - t;                  // The last step
      f(t, y, fReturn);          // Evaluate RHS's and return 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++ ) y[i] = y[i] + k2[i]; 
      t = t + h; 
      System.out.println("rk2  t=" +t+ " , x = "+y[0]+", v = "+y[1]); 
      w.println(t + " " + y[0] + " " + y[1]);       // Output to file
    }                                               // End while loop
  }     
                                    // RHS FUNCTION of your choice here
  public static void f(double t, double y[], double fReturn[])     
    { fReturn[0] = y[1];                     // RHS of first equation
      fReturn[1] = -100*y[0]-2*y[1] + 10*Math.sin(3*t); } 
}