org.apache.commons.math3.ode.nonstiff

Class DormandPrince54Integrator

java.lang.Object

org.apache.commons.math3.ode.AbstractIntegrator

org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator

org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator

org.apache.commons.math3.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

Field Summary

Fields

Modifier and Type	Field and Description
private static double	E1 Error array, element 1.
private static double	E3 Error array, element 3.
private static double	E4 Error array, element 4.
private static double	E5 Error array, element 5.
private static double	E6 Error array, element 6.
private static double	E7 Error array, element 7.
private static java.lang.String	METHOD_NAME Integrator method name.
private static double[][]	STATIC_A Internal weights Butcher array.
private static double[]	STATIC_B Propagation weights Butcher array.
private static double[]	STATIC_C Time steps Butcher array.

Fields inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator

mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance

Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator

isLastStep, resetOccurred, stepHandlers, stepSize, stepStart

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

Methods

Modifier and Type	Method and Description
protected double	estimateError(double[][] yDotK, double[] y0, double[] y1, double h) Compute the error ratio.
int	getOrder() Get the order of the method.

Methods inherited from class org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator

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

Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator

filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl

Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator

acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCounter, getCurrentSignedStepsize, getEvaluations, getEvaluationsCounter, getEventHandlers, getExpandable, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, setEquations, setMaxEvaluations, setStateInitialized

Methods inherited from class java.lang.Object

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

Field Detail

METHOD_NAME

private static final java.lang.String METHOD_NAME

Integrator method name.

See Also:

Constant Field Values

STATIC_C

private static final double[] STATIC_C

Time steps Butcher array.

STATIC_A

private static final double[][] STATIC_A

Internal weights Butcher array.

STATIC_B

private static final double[] STATIC_B

Propagation weights Butcher array.

E1

private static final double E1

Error array, element 1.

See Also:

Constant Field Values

E3

private static final double E3

Error array, element 3.

See Also:

Constant Field Values

E4

private static final double E4

Error array, element 4.

See Also:

Constant Field Values

E5

private static final double E5

Error array, element 5.

See Also:

Constant Field Values

E6

private static final double E6

Error array, element 6.

See Also:

Constant Field Values

E7

private static final double E7

Error array, element 7.

See Also:

Constant Field Values

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 (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

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 (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this

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

estimateError

protected double estimateError(double[][] yDotK,
                   double[] y0,
                   double[] y1,
                   double h)

Compute the error ratio.

Specified by:

estimateError in class EmbeddedRungeKuttaIntegrator

Parameters:

yDotK - derivatives computed during the first stages

y0 - estimate of the step at the start of the step

y1 - estimate of the step at the end of the step

h - current step

Returns:

error ratio, greater than 1 if step should be rejected