org.apache.commons.math3.ode.nonstiff
Class DormandPrince853Integrator
java.lang.Object
org.apache.commons.math3.ode.AbstractIntegrator
org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator
org.apache.commons.math3.ode.nonstiff.DormandPrince853Integrator
- All Implemented Interfaces:
- FirstOrderIntegrator, ODEIntegrator
public class DormandPrince853Integrator
- extends EmbeddedRungeKuttaIntegrator
This class implements the 8(5,3) Dormand-Prince integrator for Ordinary
Differential Equations.
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).
- Since:
- 1.2
- Version:
- $Id: DormandPrince853Integrator.java 17623 2017-05-19 07:45:31Z bignon $
Constructor Summary |
DormandPrince853Integrator(double minStep,
double maxStep,
double[] vecAbsoluteTolerance,
double[] vecRelativeTolerance)
Simple constructor. |
DormandPrince853Integrator(double minStep,
double maxStep,
double scalAbsoluteTolerance,
double scalRelativeTolerance)
Simple constructor. |
Method Summary |
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.AbstractIntegrator |
acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, integrate, setEquations, setMaxEvaluations, setStateInitialized |
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
DormandPrince853Integrator
public DormandPrince853Integrator(double minStep,
double maxStep,
double scalAbsoluteTolerance,
double scalRelativeTolerance)
- Simple constructor.
Build an eighth 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
DormandPrince853Integrator
public DormandPrince853Integrator(double minStep,
double maxStep,
double[] vecAbsoluteTolerance,
double[] vecRelativeTolerance)
- Simple constructor.
Build an eighth 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
getOrder
public int getOrder()
- Get the order of the method.
- Specified by:
getOrder
in class EmbeddedRungeKuttaIntegrator
- Returns:
- order of the method
estimateError
protected double estimateError(double[][] yDotK,
double[] y0,
double[] y1,
double h)
- Compute the error ratio.
- Specified by:
estimateError
in class EmbeddedRungeKuttaIntegrator
- 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
Copyright © 2017 CNES. All Rights Reserved.