/*
 * Leapfrog.java by Richard J. Davies
 * from `Introductory Java for Scientists and Engineers'
 * chapter: `Numerical Computation'
 * section: `Example - The Leapfrog Method'
 *
 * The program solves the ODE y' = -10y by the leapfrog
 * method with a step size of 0.001. It compares the
 * results with the analytical solution of the ODE.
 */
public class Leapfrog
{
  // Constants for the iteration
  public static final double STEPSIZE = 0.001;
  public static final int STEPS = 2000;


  // The `main' method actually implements
  // the Leapfrog method.
  public static void main(String[] argv)
  {
    // Set up array for y_n values and
    // insert initial data.
    double[] y = new double[STEPS + 1];
    y[0] = 1;

    // Perform first step by another method
    // as leapfrog needs two points.
    y[1] = y[0] - STEPSIZE * 10 * y[0];
    
    // Perform iteration
    for (int i=2; i<=STEPS; i++)
    {
      y[i] = -2 * STEPSIZE * 10 * y[i-1] + y[i-2];
      
      // Print computed value and error.
      System.out.println("At t=" + i * STEPSIZE
                 + " y estimated at " + y[i]
                 + " an error of "
                 + (y[i] - Math.exp(-10*i*STEPSIZE)));
    }
  }
}