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, 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
 

Field Summary

Fields inherited from class org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator

mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance

Constructor Summary

Constructors

Constructor and Description
DormandPrince54Integrator(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 Type	Method and Description
protected 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

filterStep, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl

Methods inherited from class org.hipparchus.ode.AbstractIntegrator

acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEquations, getEvaluations, getEvaluationsCounter, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, getStepSize, getStepStart, 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.ODEIntegrator

integrate, integrate

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

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

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)

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

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 class EmbeddedRungeKuttaIntegrator

Parameters:

forward - integration direction indicator

yDotK - slopes at the intermediate points

globalPreviousState - start of the global step

globalCurrentState - end of the global step

mapper - equations mapper for the all equations

Returns:

external weights for the high order method from Butcher array

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