///////////////////////////////////////////////////////////////////////////
//                                                                       //
// Program file name: Motion2.java                                       //
//                                                                       //
// © Tao Pang 2006                                                       //
//                                                                       //
// Last modified: January 18, 2006                                       //
//                                                                       //
// (1) This Java program is part of the book, "An Introduction to        //
//     Computational Physics, 2nd Edition," written by Tao Pang and      //
//     published by Cambridge University Press on January 19, 2006.      //
//                                                                       //
// (2) No warranties, express or implied, are made for this program.     //
//                                                                       //
///////////////////////////////////////////////////////////////////////////

// A program to study the motion of a particle under an
// elastic force in one dimension through the simplest
// predictor-corrector scheme.

import java.lang.*;
public class Motion2 {
  static final int n = 100, j = 5;
  public static void main(String argv[]) {
    double x[] = new double[n+1];
    double v[] = new double[n+1];

 // Assign time step and initial position and velocity
    double dt = 2*Math.PI/n;
    x[0] = 0;
    v[0] = 1;

 // Calculate other position and velocity recursively
    for (int i=0; i<n; ++i) {

   // Predict the next position and velocity
      x[i+1] = x[i]+v[i]*dt;
      v[i+1] = v[i]-x[i]*dt;

   // Correct the new position and velocity
      x[i+1] = x[i]+(v[i]+v[i+1])*dt/2;
      v[i+1] = v[i]-(x[i]+x[i+1])*dt/2;
    }

 // Output the result in every j time steps
    double t = 0;
    double jdt = j*dt;
    for (int i=0; i<=n; i+=j) {
      System.out.println(t +" " + x[i] +" " + v[i]);
      t += jdt;
    }
  }
}