Class DormandPrince853FieldIntegrator<T extends CalculusFieldElement<T>>
- Type Parameters:
T
- the type of the field elements
- All Implemented Interfaces:
FieldODEIntegrator<T>
,FieldButcherArrayProvider<T>
,FieldExplicitRungeKuttaIntegrator<T>
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).
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Field Summary
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Constructor Summary
ConstructorDescriptionDormandPrince853FieldIntegrator
(Field<T> field, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Simple constructor.DormandPrince853FieldIntegrator
(Field<T> field, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Simple constructor. -
Method Summary
Modifier and TypeMethodDescriptionprotected org.hipparchus.ode.nonstiff.DormandPrince853FieldStateInterpolator<T>
createInterpolator
(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper) Create an interpolator.protected double
estimateError
(T[][] yDotK, T[] y0, T[] y1, T h) Compute the error ratio.T[][]
getA()
Get the internal weights from Butcher array (without the first empty row).T[]
getB()
Get the external weights for the high order method from Butcher array.T[]
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.EmbeddedRungeKuttaFieldIntegrator
getMaxGrowth, getMinReduction, getNumberOfStages, getSafety, initIntegration, integrate, isUsingFieldCoefficients, setMaxGrowth, setMinReduction, setSafety, setUsingFieldCoefficients
Methods inherited from class org.hipparchus.ode.nonstiff.AdaptiveStepsizeFieldIntegrator
getMaxStep, getMinStep, getStepSizeHelper, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
Methods inherited from class org.hipparchus.ode.AbstractFieldIntegrator
acceptStep, addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEquations, getEvaluations, getEvaluationsCounter, getEventDetectors, getField, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepSize, getStepStart, incrementEvaluations, 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.FieldExplicitRungeKuttaIntegrator
getRealA, getRealB, getRealC, singleStep
Methods inherited from interface org.hipparchus.ode.FieldODEIntegrator
addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, getCurrentSignedStepsize, getEvaluations, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepStart, 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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DormandPrince853FieldIntegrator
public DormandPrince853FieldIntegrator(Field<T> field, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Simple constructor. Build an eighth order Dormand-Prince integrator with the given step bounds- Parameters:
field
- field to which the time and state vector elements belongminStep
- 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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DormandPrince853FieldIntegrator
public DormandPrince853FieldIntegrator(Field<T> field, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Simple constructor. Build an eighth order Dormand-Prince integrator with the given step bounds- Parameters:
field
- field to which the time and state vector elements belongminStep
- 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
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
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
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.DormandPrince853FieldStateInterpolator<T> createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper) Create an interpolator.- Specified by:
createInterpolator
in classEmbeddedRungeKuttaFieldIntegrator<T extends CalculusFieldElement<T>>
- 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 classEmbeddedRungeKuttaFieldIntegrator<T extends CalculusFieldElement<T>>
- Returns:
- order of the method
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estimateError
Compute the error ratio.- Specified by:
estimateError
in classEmbeddedRungeKuttaFieldIntegrator<T extends CalculusFieldElement<T>>
- 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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