Milne.java
package nl.tudelft.simulation.jstats.ode.integrators;
import nl.tudelft.simulation.jstats.ode.DifferentialEquationInterface;
/**
* The Milne numerical estimator as described in <a href="https://mathworld.wolfram.com/MilnesMethod.html">
* https://mathworld.wolfram.com/MilnesMethod.html </a>
* <p>
* Copyright (c) 2002-2024 Delft University of Technology, Jaffalaan 5, 2628 BX Delft, the Netherlands. All rights reserved. See
* for project information <a href="https://simulation.tudelft.nl/" target="_blank"> https://simulation.tudelft.nl</a>. The DSOL
* project is distributed under a three-clause BSD-style license, which can be found at
* <a href="https://https://simulation.tudelft.nl/dsol/docs/latest/license.html" target="_blank">
* https://https://simulation.tudelft.nl/dsol/docs/latest/license.html</a>.
* </p>
* @author <a href="https://www.tudelft.nl/averbraeck" target="_blank"> Alexander Verbraeck</a>
* @author <a href="https://www.linkedin.com/in/peterhmjacobs">Peter Jacobs </a>
*/
public class Milne extends CachingNumericalIntegrator
{
/** */
private static final long serialVersionUID = 1L;
/**
* constructs a new Milne integrator.
* @param stepSize double; the stepSize to use in the estimation.
* @param equation DifferentialEquationInterface; the equation to use.
*/
public Milne(final double stepSize, final DifferentialEquationInterface equation)
{
super(stepSize, equation, 4, NumericalIntegratorType.RUNGEKUTTA4, 10);
}
/**
* constructs a new Milne integrator, indicating the starting method and number of substeps.
* @param stepSize double; the stepSize to use in the estimation.
* @param equation DifferentialEquationInterface; the equation to use.
* @param primerIntegrationMethod NumericalIntegratorType; the primer integrator to use
* @param startingSubSteps int; the number of substeps per timestep during starting of the integrator
*/
public Milne(final double stepSize, final DifferentialEquationInterface equation,
final NumericalIntegratorType primerIntegrationMethod, final int startingSubSteps)
{
super(stepSize, equation, 4, primerIntegrationMethod, startingSubSteps);
}
/** {@inheritDoc} */
@Override
public double[] next(final double x)
{
double[] y3 = getY(3);
double[] y1 = getY(1);
double[] dy2 = getDY(2);
double[] dy1 = getDY(1);
double[] dy0 = getDY(0);
// Let's evaluate the predictor
double[] p =
add(y3, multiply(4 * this.stepSize / 3.0, add(multiply(2.0, dy0), multiply(-1.0, dy1), multiply(2.0, dy2))));
// Now we compute the corrector
return add(y1, multiply(this.stepSize / 3.0,
add(multiply(1.0, dy1), multiply(4.0, dy0), this.equation.dy(x + this.stepSize, p))));
}
}