ptolemy.domains.continuous.kernel.solver
Class ExplicitRK23Solver

java.lang.Object
  ptolemy.domains.continuous.kernel.ContinuousODESolver
      ptolemy.domains.continuous.kernel.solver.ExplicitRK23Solver

public class ExplicitRK23Solver
extends ContinuousODESolver

This class implements the Explicit Runge-Kutta 2(3) ODE solving method. For an ODE of the form:

 dx/dt = f(x, t), x(0) = x0
 

it does the following:

 K0 = f(x(n), tn);
 K1 = f(x(n)+0.5*h*K0, tn+0.5*h);
 K2 = f(x(n)+0.75*h*K1, tn+0.75*h);
 x(n+1) = x(n)+(2/9)*h*K0+(1/3)*h*K0+(4/9)*h*K2;
 K3 = f(x(n+1), tn+h);
 

, and error control:

 LTE = h*[(-5.0/72.0)*K0 + (1.0/12.0)*K1 + (1.0/9.0)*K2 + (-1.0/8.0)*K3]
 

If the LTE is less than the error tolerance, then this step is considered successful, and the next integration step is predicted as:

 h' = 0.8*Math.pow((ErrorTolerance/LTE), 1.0/3.0)
 

This is a second order method, but uses a third order procedure to estimate the local truncation error.

Since:

Ptolemy II 6.0

Version:

$Id: ExplicitRK23Solver.java 57040 2010-01-27 20:52:32Z cxh $

Author:

Jie Liu, Haiyang Zheng, Edward A. Lee

Accepted Rating:

Green (hyzheng)

Proposed Rating:

Green (hyzheng)

Field Summary

private static double[][]	_B B coefficients.
private static double[]	_E E coefficients.
private static int	_ERROR_INDEX The index of the error stored in the auxiliary variables.
private static int	_ORDER The order of the algorithm.
private int	_roundCount The round counter.
protected static double[]	_TIME_INCREMENTS The ratio of time increments within one integration step.

Fields inherited from class ptolemy.domains.continuous.kernel.ContinuousODESolver

_director

Constructor Summary

ExplicitRK23Solver()

Method Summary

protected int	_getRound() Return the current round.
protected double	_getRoundTimeIncrement() Get the current round factor.
protected boolean	_isStepFinished() Return true if the current integration step is finished.
protected void	_reset() Reset the solver, indicating to it that we are starting an integration step.
protected void	_setRound(int round) Set the round for the next integration step.
int	getIntegratorAuxVariableCount() Return the number of time increments plus one (to store the truncation error).
void	integratorIntegrate(ContinuousIntegrator integrator) Fire the given integrator.
boolean	integratorIsAccurate(ContinuousIntegrator integrator) Return true if the integration is accurate for the given integrator.
double	integratorSuggestedStepSize(ContinuousIntegrator integrator) Provide the predictedStepSize() method for the integrators under this solver.

Methods inherited from class ptolemy.domains.continuous.kernel.ContinuousODESolver

_debug, _isDebugging, _makeSolverOf

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

_TIME_INCREMENTS

protected static final double[] _TIME_INCREMENTS

The ratio of time increments within one integration step.

_B

private static final double[][] _B

B coefficients.

_E

private static final double[] _E

E coefficients.

_ERROR_INDEX

private static final int _ERROR_INDEX

The index of the error stored in the auxiliary variables.

_ORDER

private static final int _ORDER

The order of the algorithm.

See Also:

Constant Field Values

_roundCount

private int _roundCount

The round counter.

Constructor Detail

ExplicitRK23Solver

public ExplicitRK23Solver()

Method Detail

getIntegratorAuxVariableCount

public final int getIntegratorAuxVariableCount()

Return the number of time increments plus one (to store the truncation error).

Specified by:

getIntegratorAuxVariableCount in class ContinuousODESolver

Returns:

The number of time increments plus one.

integratorIntegrate

public void integratorIntegrate(ContinuousIntegrator integrator)
                         throws IllegalActionException

Fire the given integrator. This method performs the ODE solving algorithm described in the class comment.

Specified by:

integratorIntegrate in class ContinuousODESolver

Parameters:

integrator - The integrator of that calls this method.

Throws:

IllegalActionException - If there is no director, or can not read input, or can not send output.

integratorIsAccurate

public boolean integratorIsAccurate(ContinuousIntegrator integrator)

Return true if the integration is accurate for the given integrator. This estimates the local truncation error for that integrator and compare it with the error tolerance.

Specified by:

integratorIsAccurate in class ContinuousODESolver

Parameters:

integrator - The integrator of that calls this method.

Returns:

True if the integration is successful.

integratorSuggestedStepSize

public double integratorSuggestedStepSize(ContinuousIntegrator integrator)

Provide the predictedStepSize() method for the integrators under this solver. It uses the algorithm in the class comments to predict the next step size based on the current estimation of the local truncation error.

Specified by:

integratorSuggestedStepSize in class ContinuousODESolver

Parameters:

integrator - The integrator of that calls this method.

Returns:

The next step size suggested by the given integrator.

_getRound

protected int _getRound()

Return the current round.

Specified by:

_getRound in class ContinuousODESolver

Returns:

The current round.

_getRoundTimeIncrement

protected final double _getRoundTimeIncrement()

Get the current round factor.

Specified by:

_getRoundTimeIncrement in class ContinuousODESolver

Returns:

The current round factor.

See Also:

ContinuousODESolver._isStepFinished()

_isStepFinished

protected final boolean _isStepFinished()

Return true if the current integration step is finished. This method will return true if _incrementRound() has been called 4 or more times since _reset().

Specified by:

_isStepFinished in class ContinuousODESolver

Returns:

Return true if the solver has finished an integration step.

See Also:

_reset()

_reset

protected final void _reset()

Reset the solver, indicating to it that we are starting an integration step. This method resets the round counter.

Specified by:

_reset in class ContinuousODESolver

_setRound

protected void _setRound(int round)

Set the round for the next integration step.

Specified by:

_setRound in class ContinuousODESolver

Parameters:

round - The round for the next integration step.

See Also:

ContinuousODESolver.getIntegratorAuxVariableCount()