ODESolverRK3

package odeadapt;

import Jama.*;

/**
 * ODESolverRK3.java
 * solves a given ODE by giving the "next" value for x 
 * using Runge-Kutta method of order 3
 */
public class ODESolverRK3 extends ODESingleStepSolver {

  /**
   * construct solver for a given ODE
   */
  public ODESolverRK3(ODE ode) {
    super(ode);
    order = 3;
  }

  /*
   * integrate until t + h
   * using a third order Runge-Kutta scheme
   */
  public int nextStep(double h) {
    Matrix k1 = ode.f(x, t);
    double t1 = t + h / 3.0;
    
    // x1 = x + h*k1/3.0;
    Matrix x1 = x.plus(k1.times(h / 3.0));
    Matrix k2 = ode.f(x1, t1);
    double t2 = t + 2.0 / 3.0 * h;
    
    // x2 = x + h*k2*2.0/3.0;
    Matrix x2 = x.plus(k2.times(h * 2.0 / 3.0));
    Matrix k3 = ode.f(x2, t2);
    
    // x += (k1 + 3.0*k3)*h/4.0;
    x.plusEquals(k1.times(h / 4.0));
    x.plusEquals(k3.times(h * 3.0 / 4.0));
    
    t += h;
    return 1;
  }
}