Package org.hipparchus.ode.nonstiff
Class DormandPrince54Integrator
java.lang.Object
org.hipparchus.ode.AbstractIntegrator
org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator
org.hipparchus.ode.nonstiff.EmbeddedRungeKuttaIntegrator
org.hipparchus.ode.nonstiff.DormandPrince54Integrator
- All Implemented Interfaces:
ButcherArrayProvider
,ExplicitRungeKuttaIntegrator
,ODEIntegrator
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
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Field Summary
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Constructor Summary
ConstructorDescriptionDormandPrince54Integrator
(double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Simple constructor.DormandPrince54Integrator
(double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Simple constructor. -
Method Summary
Modifier and TypeMethodDescriptionprotected org.hipparchus.ode.nonstiff.DormandPrince54StateInterpolator
createInterpolator
(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper) Create an interpolator.protected double
estimateError
(double[][] yDotK, double[] y0, double[] y1, double h) Compute the error ratio.double[][]
getA()
Get the internal weights from Butcher array (without the first empty row).double[]
getB()
Get the external weights for the high order method from Butcher array.double[]
getC()
Get the time steps from Butcher array (without the first zero).int
getOrder()
Get the order of the method.Methods inherited from class org.hipparchus.ode.nonstiff.EmbeddedRungeKuttaIntegrator
getMaxGrowth, getMinReduction, getSafety, integrate, setMaxGrowth, setMinReduction, setSafety
Methods inherited from class org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator
getMaxStep, getMinStep, getStepSizeHelper, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
Methods inherited from class org.hipparchus.ode.AbstractIntegrator
acceptStep, addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEquations, getEvaluations, getEvaluationsCounter, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepSize, getStepStart, incrementEvaluations, initIntegration, isLastStep, resetOccurred, setIsLastStep, setMaxEvaluations, setStateInitialized, setStepSize, setStepStart
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface org.hipparchus.ode.nonstiff.ExplicitRungeKuttaIntegrator
getNumberOfStages, singleStep
Methods inherited from interface org.hipparchus.ode.ODEIntegrator
addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, getCurrentSignedStepsize, getEvaluations, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepStart, integrate, setMaxEvaluations
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Field Details
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METHOD_NAME
Name of integration scheme.- See Also:
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Constructor Details
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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 Details
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getC
public double[] getC()Get the time steps from Butcher array (without the first zero).- Returns:
- time steps from Butcher array (without the first zero
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getA
public double[][] getA()Get the internal weights from Butcher array (without the first empty row).- Returns:
- internal weights from Butcher array (without the first empty row)
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getB
public double[] getB()Get the external weights for the high order method from Butcher array.- Returns:
- external weights for the high order method from Butcher array
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createInterpolator
protected org.hipparchus.ode.nonstiff.DormandPrince54StateInterpolator createInterpolator(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper) Create an interpolator.- Specified by:
createInterpolator
in classEmbeddedRungeKuttaIntegrator
- Parameters:
forward
- integration direction indicatoryDotK
- slopes at the intermediate pointsglobalPreviousState
- start of the global stepglobalCurrentState
- end of the global stepmapper
- equations mapper for the all equations- Returns:
- external weights for the high order method from Butcher array
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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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