Class DormandPrince54Integrator
- java.lang.Object
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- org.apache.commons.math3.ode.AbstractIntegrator
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- org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
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- org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator
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- org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator
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- 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
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Field Summary
Fields Modifier and Type Field 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
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Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator
isLastStep, resetOccurred, stepHandlers, stepSize, stepStart
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Constructor Summary
Constructors Constructor Description DormandPrince54Integrator(double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
Simple constructor.DormandPrince54Integrator(double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
Simple constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method 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
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Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
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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
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Field Detail
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METHOD_NAME
private static final java.lang.String METHOD_NAME
Integrator method name.- See Also:
- Constant Field Values
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STATIC_C
private static final double[] STATIC_C
Time steps Butcher array.
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STATIC_A
private static final double[][] STATIC_A
Internal weights Butcher array.
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STATIC_B
private static final double[] STATIC_B
Propagation weights Butcher array.
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E1
private static final double E1
Error array, element 1.- See Also:
- Constant Field Values
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E3
private static final double E3
Error array, element 3.- See Also:
- Constant Field Values
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E4
private static final double E4
Error array, element 4.- See Also:
- Constant Field Values
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E5
private static final double E5
Error array, element 5.- See Also:
- Constant Field Values
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E6
private static final double E6
Error array, element 6.- See Also:
- Constant Field Values
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E7
private static final double E7
Error array, element 7.- See Also:
- Constant Field Values
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Constructor Detail
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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 thismaxStep
- maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than thisscalAbsoluteTolerance
- allowed absolute errorscalRelativeTolerance
- allowed relative error
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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 thismaxStep
- maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than thisvecAbsoluteTolerance
- allowed absolute errorvecRelativeTolerance
- allowed relative error
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Method Detail
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getOrder
public int getOrder()
Get the order of the method.- Specified by:
getOrder
in classEmbeddedRungeKuttaIntegrator
- Returns:
- order of the method
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estimateError
protected double estimateError(double[][] yDotK, double[] y0, double[] y1, double h)
Compute the error ratio.- Specified by:
estimateError
in classEmbeddedRungeKuttaIntegrator
- Parameters:
yDotK
- derivatives computed during the first stagesy0
- estimate of the step at the start of the stepy1
- estimate of the step at the end of the steph
- current step- Returns:
- error ratio, greater than 1 if step should be rejected
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