org.apache.commons.math3.ode.nonstiff
public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator
This integrator is an embedded Runge-Kutta integrator of order 8(5,3) 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 12 functions evaluations per step for integration and 4 evaluations for interpolation. However, since the first interpolation evaluation is the same as the first integration evaluation of the next step, we have included it in the integrator rather than in the interpolator and specified the method was an fsal. Hence, despite we have 13 stages here, the cost is really 12 evaluations per step even if no interpolation is done, and the overcost of interpolation is only 3 evaluations.
This method is based on an 8(6) method by Dormand and Prince (i.e. order 8 for the integration and order 6 for error estimation) modified by Hairer and Wanner to use a 5th order error estimator with 3rd order correction. This modification was introduced because the original method failed in some cases (wrong steps can be accepted when step size is too large, for example in the Brusselator problem) and also had severe difficulties when applied to problems with discontinuities. This modification is explained in the second edition of the first volume (Nonstiff Problems) of the reference book by Hairer, Norsett and Wanner: Solving Ordinary Differential Equations (Springer-Verlag, ISBN 3-540-56670-8).
Modifier and Type | Field and Description |
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private static double |
E1_01
First error weights array, element 1.
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private static double |
E1_06
First error weights array, element 6.
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private static double |
E1_07
First error weights array, element 7.
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private static double |
E1_08
First error weights array, element 8.
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private static double |
E1_09
First error weights array, element 9.
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private static double |
E1_10
First error weights array, element 10.
|
private static double |
E1_11
First error weights array, element 11.
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private static double |
E1_12
First error weights array, element 12.
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private static double |
E2_01
Second error weights array, element 1.
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private static double |
E2_06
Second error weights array, element 6.
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private static double |
E2_07
Second error weights array, element 7.
|
private static double |
E2_08
Second error weights array, element 8.
|
private static double |
E2_09
Second error weights array, element 9.
|
private static double |
E2_10
Second error weights array, element 10.
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private static double |
E2_11
Second error weights array, element 11.
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private static double |
E2_12
Second error weights array, element 12.
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private static String |
METHOD_NAME
Integrator method name.
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private static double[][] |
STATIC_A
Internal weights Butcher array.
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private static double[] |
STATIC_B
Propagation weights Butcher array.
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private static double[] |
STATIC_C
Time steps Butcher array.
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mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance
isLastStep, resetOccurred, stepHandlers, stepSize, stepStart
Constructor and Description |
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DormandPrince853Integrator(double minStep,
double maxStep,
double[] vecAbsoluteTolerance,
double[] vecRelativeTolerance)
Simple constructor.
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DormandPrince853Integrator(double minStep,
double maxStep,
double scalAbsoluteTolerance,
double scalRelativeTolerance)
Simple constructor.
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Modifier and Type | Method and Description |
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protected double |
estimateError(double[][] yDotK,
double[] y0,
double[] y1,
double h)
Compute the error ratio.
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int |
getOrder()
Get the order of the method.
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getMaxGrowth, getMinReduction, getSafety, integrate, setMaxGrowth, setMinReduction, setSafety
filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, setEquations, setMaxEvaluations, setStateInitialized
private static final String METHOD_NAME
private static final double[] STATIC_C
private static final double[][] STATIC_A
private static final double[] STATIC_B
private static final double E1_01
private static final double E1_06
private static final double E1_07
private static final double E1_08
private static final double E1_09
private static final double E1_10
private static final double E1_11
private static final double E1_12
private static final double E2_01
private static final double E2_06
private static final double E2_07
private static final double E2_08
private static final double E2_09
private static final double E2_10
private static final double E2_11
private static final double E2_12
public DormandPrince853Integrator(double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
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 errorpublic DormandPrince853Integrator(double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
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 errorpublic int getOrder()
getOrder
in class EmbeddedRungeKuttaIntegrator
protected double estimateError(double[][] yDotK, double[] y0, double[] y1, double h)
estimateError
in class EmbeddedRungeKuttaIntegrator
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 stepCopyright (c) 2003-2013 Apache Software Foundation