org.apache.commons.math.ode.nonstiff

Class DormandPrince54Integrator

java.lang.Object

org.apache.commons.math.ode.AbstractIntegrator

org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator

org.apache.commons.math.ode.nonstiff.EmbeddedRungeKuttaIntegrator

org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

All Implemented Interfaces:

FirstOrderIntegrator, ODEIntegrator

public class DormandPrince54Integrator
extends EmbeddedRungeKuttaIntegrator

This class implements the 5(4) Dormand-Prince integrator for Ordinary Differential Equations.

This integrator is an embedded Runge-Kutta integrator of order 5(4) used in local extrapolation mode (i.e. the solution is computed using the high order formula) with stepsize control (and automatic step initialization) and continuous output. This method uses 7 functions evaluations per step. However, since this is an fsal, the last evaluation of one step is the same as the first evaluation of the next step and hence can be avoided. So the cost is really 6 functions evaluations per step.

This method has been published (whithout the continuous output that was added by Shampine in 1986) in the following article :

  A family of embedded Runge-Kutta formulae
  J. R. Dormand and P. J. Prince
  Journal of Computational and Applied Mathematics
  volume 6, no 1, 1980, pp. 19-26
 

Since:

1.2

Constructor Summary

Constructors

Constructor and Description
DormandPrince54Integrator(double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Simple constructor.
DormandPrince54Integrator(double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Simple constructor.

Method Summary

Modifier and Type	Method and Description
int	getOrder() Get the order of the method.

Methods inherited from class org.apache.commons.math.ode.nonstiff.EmbeddedRungeKuttaIntegrator

getMaxGrowth, getMinReduction, getSafety, integrate, setMaxGrowth, setMinReduction, setSafety

Methods inherited from class org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator

getCurrentStepStart, getMaxStep, getMinStep, initializeStep, setInitialStepSize

Methods inherited from class org.apache.commons.math.ode.AbstractIntegrator

addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, setMaxEvaluations

Methods inherited from class java.lang.Object

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

Constructor Detail

DormandPrince54Integrator

public DormandPrince54Integrator(double minStep,
                                 double maxStep,
                                 double scalAbsoluteTolerance,
                                 double scalRelativeTolerance)

Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds

Parameters:

minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this

maxStep - maximal step (must be positive even for backward integration)

scalAbsoluteTolerance - allowed absolute error

scalRelativeTolerance - allowed relative error

DormandPrince54Integrator

public DormandPrince54Integrator(double minStep,
                                 double maxStep,
                                 double[] vecAbsoluteTolerance,
                                 double[] vecRelativeTolerance)

Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds

Parameters:

minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this

maxStep - maximal step (must be positive even for backward integration)

vecAbsoluteTolerance - allowed absolute error

vecRelativeTolerance - allowed relative error

Method Detail

getOrder

public int getOrder()

Get the order of the method.

Specified by:

getOrder in class EmbeddedRungeKuttaIntegrator

Returns:

order of the method