org.apache.commons.math3.ode.nonstiff
Class DormandPrince54Integrator

java.lang.Object
  extended by org.apache.commons.math3.ode.AbstractIntegrator
      extended by org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
          extended by org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaIntegrator
              extended by org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator
All Implemented Interfaces:
FirstOrderIntegrator, ODEIntegrator

public class DormandPrince54Integrator
extends EmbeddedRungeKuttaIntegrator

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
 

Since:
1.2
Version:
$Id: DormandPrince54Integrator.java 1416643 2012-12-03 19:37:14Z tn $

Field Summary
 
Fields inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance
 
Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator
isLastStep, resetOccurred, stepHandlers, stepSize, stepStart
 
Constructor Summary
DormandPrince54Integrator(double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
          Simple constructor.
DormandPrince54Integrator(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.nonstiff.EmbeddedRungeKuttaIntegrator
getMaxGrowth, getMinReduction, getSafety, integrate, setMaxGrowth, setMinReduction, setSafety
 
Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
 
Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator
acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, setEquations, setMaxEvaluations, setStateInitialized
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

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 this
maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
scalAbsoluteTolerance - allowed absolute error
scalRelativeTolerance - allowed relative error

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 this
maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
vecAbsoluteTolerance - allowed absolute error
vecRelativeTolerance - allowed relative error
Method Detail

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 stages
y0 - estimate of the step at the start of the step
y1 - estimate of the step at the end of the step
h - current step
Returns:
error ratio, greater than 1 if step should be rejected


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