ODESolverRalston

package odend;

import Jama.*;

/**
 * solver using Ralston method
 */
public class ODESolverRalston extends ODESolver {

  /** sets ode and initial values */
  public ODESolverRalston(ODE ode) {
    super(ode);
  }

  /** computes solution at next time step<br>
   * using the 2nd order Ralston scheme
   */
  public void nextStep(double h) {
    Matrix k1 = ode.f(x, t);
    
    double t1 = t + 3.0 / 4.0 * h;
    Matrix x1 = x.plus(k1.times(3.0 / 4.0 * h)); // x1 = x + 3.0/4.0*h*k1
    Matrix k2 = ode.f(x1, t1);
    
    // x += (1.0/3.0*k1 + 2.0/3.0*k2)*h
    x.plusEquals(k1.times(h / 3.0));
    x.plusEquals(k2.times(h * 2.0 / 3.0));
    
    t += h;
  }
}