public class DormandPrince853Integrator extends RungeKuttaFehlbergIntegrator
This integrator is an embedded Runge-Kutta-Fehlberg 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).
handler, scalAbsoluteTolerance, scalRelativeTolerance, stepSize, stepStart, switchesHandler, vecAbsoluteTolerance, vecRelativeTolerance| 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 |
|---|---|
protected double |
estimateError(double[][] yDotK,
double[] y0,
double[] y1,
double h)
Compute the error ratio.
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java.lang.String |
getName()
Get the name of the method.
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int |
getOrder()
Get the order of the method.
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getMaxGrowth, getMinReduction, getSafety, integrate, setMaxGrowth, setMinReduction, setSafetyaddSwitchingFunction, filterStep, getCurrentStepsize, getCurrentStepStart, getMaxStep, getMinStep, getStepHandler, initializeStep, resetInternalState, setInitialStepSize, setStepHandlerpublic DormandPrince853Integrator(double minStep,
double maxStep,
double scalAbsoluteTolerance,
double scalRelativeTolerance)
minStep - minimal step (must be positive even for backward
integration), the last step can be smaller than thismaxStep - maximal step (must be positive even for backward
integration)scalAbsoluteTolerance - allowed absolute errorscalRelativeTolerance - allowed relative errorpublic DormandPrince853Integrator(double minStep,
double maxStep,
double[] vecAbsoluteTolerance,
double[] vecRelativeTolerance)
minStep - minimal step (must be positive even for backward
integration), the last step can be smaller than thismaxStep - maximal step (must be positive even for backward
integration)vecAbsoluteTolerance - allowed absolute errorvecRelativeTolerance - allowed relative errorpublic java.lang.String getName()
getName in interface FirstOrderIntegratorgetName in class RungeKuttaFehlbergIntegratorpublic int getOrder()
getOrder in class RungeKuttaFehlbergIntegratorprotected double estimateError(double[][] yDotK,
double[] y0,
double[] y1,
double h)
estimateError in class RungeKuttaFehlbergIntegratoryDotK - 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 © 2001-2007 Luc Maisonobe. All Rights Reserved.