Apache Commons Math 3.6.1 · org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator

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

Field Summary

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

Constructor Summary

Access	Constructor and Description
public	DormandPrince54Integrator(final double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this minStep, final double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep, final double allowed absolute error scalAbsoluteTolerance, final double allowed relative error scalRelativeTolerance) Simple constructor.
public	DormandPrince54Integrator(final double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this minStep, final double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep, final double[] allowed absolute error vecAbsoluteTolerance, final double[] allowed relative error vecRelativeTolerance) Simple constructor.

Access

Constructor and Description

public

DormandPrince54Integrator(final double

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

minStep, final double

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

maxStep, final double

allowed absolute error

scalAbsoluteTolerance, final double

allowed relative error

scalRelativeTolerance)

Simple constructor.

public

DormandPrince54Integrator(final double

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

minStep, final double

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

maxStep, final double[]

allowed absolute error

vecAbsoluteTolerance, final double[]

allowed relative error

vecRelativeTolerance)

Simple constructor.

Method Summary

Modifier and Type	Method and Description
protected double	estimateError(final double[][] derivatives computed during the first stages yDotK, final double[] estimate of the step at the start of the step y0, final double[] estimate of the step at the end of the step y1, final double current step h) Implements abstract org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.estimateError. Compute the error ratio.
public int	getOrder() Implements abstract org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.getOrder. Get the order of the method.

Inherited from org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator:: getMaxGrowth getMinReduction getSafety integrate setMaxGrowth setMinReduction setSafety

Field Detail

E1	back to summary
private static final double E1 Error array, element 1.

E3	back to summary
private static final double E3 Error array, element 3.

E4	back to summary
private static final double E4 Error array, element 4.

E5	back to summary
private static final double E5 Error array, element 5.

E6	back to summary
private static final double E6 Error array, element 6.

E7	back to summary
private static final double E7 Error array, element 7.

METHOD_NAME	back to summary
private static final String METHOD_NAME Integrator method name.

STATIC_A	back to summary
private static final double[][] STATIC_A Internal weights Butcher array.

STATIC_B	back to summary
private static final double[] STATIC_B Propagation weights Butcher array.

STATIC_C	back to summary
private static final double[] STATIC_C Time steps Butcher array.

Constructor Detail

DormandPrince54Integrator	back to summary
public DormandPrince54Integrator(final double minStep, final double maxStep, final double scalAbsoluteTolerance, final double scalRelativeTolerance) Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds Parameters minStep:double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep:double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this scalAbsoluteTolerance:double allowed absolute error scalRelativeTolerance:double allowed relative error

DormandPrince54Integrator

back to summary

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

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

Parameters

minStep:double: minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
maxStep:double: maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
scalAbsoluteTolerance:double: allowed absolute error
scalRelativeTolerance:double: allowed relative error

DormandPrince54Integrator	back to summary
public DormandPrince54Integrator(final double minStep, final double maxStep, final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance) Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds Parameters minStep:double minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this maxStep:double maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this vecAbsoluteTolerance:double[] allowed absolute error vecRelativeTolerance:double[] allowed relative error

DormandPrince54Integrator

back to summary

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

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

Parameters

minStep:double: minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
maxStep:double: maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
vecAbsoluteTolerance:double[]: allowed absolute error
vecRelativeTolerance:double[]: allowed relative error

Method Detail

estimateError	back to summary
protected double estimateError(final double[][] yDotK, final double[] y0, final double[] y1, final double h) Implements abstract org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.estimateError. Doc from org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.estimateError. Compute the error ratio. Parameters yDotK:double[][] derivatives computed during the first stages y0:double[] estimate of the step at the start of the step y1:double[] estimate of the step at the end of the step h:double current step Returns:double error ratio, greater than 1 if step should be rejected Annotations @Override

estimateError

back to summary

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

Implements abstract org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.estimateError.

Doc from org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.estimateError.

Compute the error ratio.

Parameters

yDotK:double[][]: derivatives computed during the first stages
y0:double[]: estimate of the step at the start of the step
y1:double[]: estimate of the step at the end of the step
h:double: current step

Returns:double

error ratio, greater than 1 if step should be rejected

Annotations

@Override

getOrder	back to summary
public int getOrder() Implements abstract org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.getOrder. Doc from org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.getOrder. Get the order of the method. Returns:int order of the method Annotations @Override

getOrder

back to summary

public int getOrder()

Implements abstract org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.getOrder.

Doc from org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator.getOrder.

Get the order of the method.

Returns:int

order of the method

Annotations

@Override

public Class DormandPrince54Integrator

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail