ptolemy.domains.ct.kernel.solver
Class ExplicitRK45Solver

java.lang.Object
  ptolemy.kernel.util.NamedObj
      ptolemy.domains.ct.kernel.ODESolver
          ptolemy.domains.ct.kernel.solver.ExplicitRK45Solver

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, Changeable, Debuggable, DebugListener, Derivable, ModelErrorHandler, MoMLExportable, Moveable, Nameable

public class ExplicitRK45Solver
extends ODESolver

This class implements a fourth-order Runge-Kutta ODE solving method. The algorithm was introduced in "A Variable Order Runge-Kutta Method for Initial Value Problems with Rapidly Varying Right-Hand Sides" by J. R. Cash and Alan H. Karp, ACM Transactions on Mathematical Software, vol 16, pp. 201-222, 1990. For completeness, a brief explanation of the algorithm is explained below.

For an ODE of the form:

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

it does the following:

 K0 = f(x(n), tn);
 K1 = f(x(n) + 0.2*K0*h, tn + 0.2*h);
 K2 = f(x(n) + (3.0/40*K0 + 9.0/40*K1)*h, tn + 0.3*h);
 K3 = f(x(n) + (0.3*K0 - 0.9*K1 + 1.2*K2)*h, tn + 0.6*h);
 K4 = f(x(n) + (-11/54*K0 + 5.0/2*K1 -70/27*K2 + 35/27*K3)*h, tn + 1.0*h);
 K5 = f(x(n) + (1631/55296*K0 + 175/512*K1 + 575/13824*K2 + 3544275/110592*K3
 + 253/4096*K4)*h, tn + 7/8*h);
 x(n+1) = x(n)+(37/378*K0 + 250/621*K2 + 125.0/594*K3 + 512.0/1771*K5)*h;
 

, and error control:

 LTE = [(37.0/378 - 2825.0/27648)*K0 + (250.0/621 - 18575.0/48384)*K2 +
 (125.0/594 - 13525.0/55296)*K3 + (0.0 - 277.0/14336)*K4 +
 (512.0/1771 - 0.25)*K5]*h.
 

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

 h' = h * Math.pow((ErrorTolerance/LTE), 1.0/5.0)
 

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

It takes 6 steps for this solver to resolve a state with an integration step size. A round counter is used to record which step this solver performs.

Since:

Ptolemy II 4.1

Version:

$Id: ExplicitRK45Solver.java 57040 2010-01-27 20:52:32Z cxh $

Author:

Haiyang Zheng

See Also:

Serialized Form

Accepted Rating:

Green (hyzheng)

Proposed Rating:

Green (hyzheng)

Nested Class Summary

Nested classes/interfaces inherited from class ptolemy.kernel.util.NamedObj

NamedObj.ContainedObjectsIterator

Field Summary

private static double[][]	_B B coefficients
private static java.lang.String	_DEFAULT_NAME The name of the solver
private static double[]	_E E coefficients
private static int	_order The order of the algorithm.
private static double[]	_timeInc The ratio of time increments within one integration step.

Fields inherited from class ptolemy.kernel.util.NamedObj

_changeListeners, _changeLock, _changeRequests, _debugging, _debugListeners, _elementName, _isPersistent, _verbose, _workspace, ATTRIBUTES, CLASSNAME, COMPLETE, CONTENTS, DEEP, FULLNAME, LINKS

Constructor Summary

ExplicitRK45Solver()
Construct a solver in the default workspace.

ExplicitRK45Solver(Workspace workspace)
Construct a solver in the given workspace.

Method Summary

protected void	_advanceModelTime() Override the method in the base abstract class to advance the model time.
void	fireStateTransitionActors() Fire state transition actors.
int	getAmountOfHistoryInformation() Return 0 to indicate that no history information is needed by this solver.
int	getIntegratorAuxVariableCount() Return 7 to indicate that 7 auxiliary variables are needed by this solver.
void	integratorFire(CTBaseIntegrator integrator) Fire the given integrator.
boolean	integratorIsAccurate(CTBaseIntegrator integrator) Return true if the integration is accurate for the given integrator.
double	integratorPredictedStepSize(CTBaseIntegrator integrator) Predict the next step size for the integrators executed under this solver.

Methods inherited from class ptolemy.domains.ct.kernel.ODESolver

_getRoundCount, _getSchedule, _incrementRoundCount, _isConverged, _makeSolverOf, _resetRoundCount, _setConverged, _voteForConverged, fireDynamicActors, getContainer, resolveStates

Methods inherited from class ptolemy.kernel.util.NamedObj

_addAttribute, _adjustOverride, _attachText, _cloneFixAttributeFields, _debug, _debug, _debug, _debug, _debug, _description, _exportMoMLContents, _getContainedObject, _getIndentPrefix, _isMoMLSuppressed, _markContentsDerived, _propagateExistence, _propagateValue, _recordDecoratedAttributes, _removeAttribute, _splitName, _stripNumericSuffix, _validateSettables, addChangeListener, addDebugListener, attributeChanged, attributeList, attributeList, attributeTypeChanged, clone, clone, containedObjectsIterator, deepContains, depthInHierarchy, description, description, event, executeChangeRequests, exportMoML, exportMoML, exportMoML, exportMoML, exportMoML, exportMoMLPlain, getAttribute, getAttribute, getAttributes, getChangeListeners, getClassName, getDecoratorAttribute, getDecoratorAttributes, getDerivedLevel, getDerivedList, getDisplayName, getElementName, getFullName, getModelErrorHandler, getName, getName, getPrototypeList, getSource, handleModelError, isDeferringChangeRequests, isOverridden, isPersistent, lazyContainedObjectsIterator, message, moveDown, moveToFirst, moveToIndex, moveToLast, moveUp, propagateExistence, propagateValue, propagateValues, removeChangeListener, removeDebugListener, requestChange, setClassName, setDeferringChangeRequests, setDerivedLevel, setDisplayName, setModelErrorHandler, setName, setPersistent, setSource, sortContainedObjects, toplevel, toString, uniqueName, validateSettables, workspace

Methods inherited from class java.lang.Object

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

Field Detail

_DEFAULT_NAME

private static final java.lang.String _DEFAULT_NAME

The name of the solver

See Also:

Constant Field Values

_timeInc

private static final double[] _timeInc

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

_order

private static final int _order

The order of the algorithm.

See Also:

Constant Field Values

Constructor Detail

ExplicitRK45Solver

public ExplicitRK45Solver()

Construct a solver in the default workspace. The solver is added to the list of objects in the workspace. Increment the version number of the workspace. The name of the solver is set to "CT_Runge_Kutta_4_5_Solver".

ExplicitRK45Solver

public ExplicitRK45Solver(Workspace workspace)

Construct a solver in the given workspace. If the workspace argument is null, use the default workspace. The director is added to the list of objects in the workspace. Increment the version number of the workspace. The name of the solver is set to "CT_Runge_Kutta_4_5_Solver".

Parameters:

workspace - Object for synchronization and version tracking.

Method Detail

fireStateTransitionActors

public void fireStateTransitionActors()
                               throws IllegalActionException

Fire state transition actors. Increment the round count. If the current round is the last (sixth) round, set converged flag to true indicating the fixed-point states have been reached. Reset the round count if the current round is the last round.

Overrides:

fireStateTransitionActors in class ODESolver

Throws:

IllegalActionException - If thrown in the super class.

getAmountOfHistoryInformation

public final int getAmountOfHistoryInformation()

Return 0 to indicate that no history information is needed by this solver.

Specified by:

getAmountOfHistoryInformation in class ODESolver

Returns:

0.

getIntegratorAuxVariableCount

public final int getIntegratorAuxVariableCount()

Return 7 to indicate that 7 auxiliary variables are needed by this solver.

Specified by:

getIntegratorAuxVariableCount in class ODESolver

Returns:

7.

integratorFire

public void integratorFire(CTBaseIntegrator integrator)
                    throws IllegalActionException

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

Specified by:

integratorFire in class ODESolver

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(CTBaseIntegrator 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 ODESolver

Parameters:

integrator - The integrator of that calls this method.

Returns:

True if the integration is successful.

integratorPredictedStepSize

public double integratorPredictedStepSize(CTBaseIntegrator integrator)

Predict the next step size for the integrators executed 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:

integratorPredictedStepSize in class ODESolver

Parameters:

integrator - The integrator that calls this method.

Returns:

The next step size suggested by the given integrator.

_advanceModelTime

protected void _advanceModelTime()
                          throws IllegalActionException

Override the method in the base abstract class to advance the model time. The amount of the increment is decided by the number of the round counter and the current step size.

Overrides:

_advanceModelTime in class ODESolver

Throws:

IllegalActionException - If thrown in the super class or the model time can not be set.