Package org.hipparchus.ode.nonstiff

Class EmbeddedRungeKuttaIntegrator

java.lang.Object

org.hipparchus.ode.AbstractIntegrator

org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator

org.hipparchus.ode.nonstiff.EmbeddedRungeKuttaIntegrator

All Implemented Interfaces:

ButcherArrayProvider, ODEIntegrator

Direct Known Subclasses:

DormandPrince54Integrator, DormandPrince853Integrator, HighamHall54Integrator

public abstract class EmbeddedRungeKuttaIntegrator
extends AdaptiveStepsizeIntegrator
implements ButcherArrayProvider

This class implements the common part of all embedded Runge-Kutta integrators for Ordinary Differential Equations.

These methods are embedded explicit Runge-Kutta methods with two sets of coefficients allowing to estimate the error, their Butcher arrays are as follows :

    0  |
   c2  | a21
   c3  | a31  a32
   ... |        ...
   cs  | as1  as2  ...  ass-1
       |--------------------------
       |  b1   b2  ...   bs-1  bs
       |  b'1  b'2 ...   b's-1 b's
 

In fact, we rather use the array defined by ej = bj - b'j to compute directly the error rather than computing two estimates and then comparing them.

Some methods are qualified as fsal (first same as last) methods. This means the last evaluation of the derivatives in one step is the same as the first in the next step. Then, this evaluation can be reused from one step to the next one and the cost of such a method is really s-1 evaluations despite the method still has s stages. This behaviour is true only for successful steps, if the step is rejected after the error estimation phase, no evaluation is saved. For an fsal method, we have cs = 1 and asi = bi for all i.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	EmbeddedRungeKuttaIntegrator(String name, int fsal, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)	Build a Runge-Kutta integrator with the given Butcher array.
protected	EmbeddedRungeKuttaIntegrator(String name, int fsal, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)	Build a Runge-Kutta integrator with the given Butcher array.

Method Summary

Modifier and Type	Method	Description
protected abstract org.hipparchus.ode.nonstiff.RungeKuttaStateInterpolator	createInterpolator(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper)	Create an interpolator.
protected abstract double	estimateError(double[][] yDotK, double[] y0, double[] y1, double h)	Compute the error ratio.
double	getMaxGrowth()	Get the maximal growth factor for stepsize control.
double	getMinReduction()	Get the minimal reduction factor for stepsize control.
abstract int	getOrder()	Get the order of the method.
double	getSafety()	Get the safety factor for stepsize control.
ODEStateAndDerivative	integrate(ExpandableODE equations, ODEState initialState, double finalTime)	Integrate the differential equations up to the given time.
void	setMaxGrowth(double maxGrowth)	Set the maximal growth factor for stepsize control.
void	setMinReduction(double minReduction)	Set the minimal reduction factor for stepsize control.
void	setSafety(double safety)	Set the safety factor for stepsize control.

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, 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.ButcherArrayProvider

getA, getB, getC

Methods inherited from interface org.hipparchus.ode.ODEIntegrator

integrate

Constructor Detail

EmbeddedRungeKuttaIntegrator

protected EmbeddedRungeKuttaIntegrator(String name,
                                       int fsal,
                                       double minStep,
                                       double maxStep,
                                       double scalAbsoluteTolerance,
                                       double scalRelativeTolerance)

Build a Runge-Kutta integrator with the given Butcher array.

Parameters:

name - name of the method

fsal - index of the pre-computed derivative for fsal methods or -1 if method is not fsal

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

EmbeddedRungeKuttaIntegrator

protected EmbeddedRungeKuttaIntegrator(String name,
                                       int fsal,
                                       double minStep,
                                       double maxStep,
                                       double[] vecAbsoluteTolerance,
                                       double[] vecRelativeTolerance)

Build a Runge-Kutta integrator with the given Butcher array.

Parameters:

name - name of the method

fsal - index of the pre-computed derivative for fsal methods or -1 if method is not fsal

minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this

maxStep - maximal step (must be positive even for backward integration)

vecAbsoluteTolerance - allowed absolute error

vecRelativeTolerance - allowed relative error

Method Detail

createInterpolator

protected abstract org.hipparchus.ode.nonstiff.RungeKuttaStateInterpolator createInterpolator(boolean forward,
                                                                                              double[][] yDotK,
                                                                                              ODEStateAndDerivative globalPreviousState,
                                                                                              ODEStateAndDerivative globalCurrentState,
                                                                                              EquationsMapper mapper)

Create an interpolator.

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 abstract int getOrder()

Get the order of the method.

Returns:

order of the method

getSafety

public double getSafety()

Get the safety factor for stepsize control.

Returns:

safety factor

setSafety

public void setSafety(double safety)

Set the safety factor for stepsize control.

Parameters:

safety - safety factor

integrate

public ODEStateAndDerivative integrate(ExpandableODE equations,
                                       ODEState initialState,
                                       double finalTime)
                                throws MathIllegalArgumentException,
                                       MathIllegalStateException

Integrate the differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

Since this method stores some internal state variables made available in its public interface during integration (ODEIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

Specified by:

integrate in interface ODEIntegrator

Parameters:

equations - differential equations to integrate

initialState - initial state (time, primary and secondary state vectors)

finalTime - target time for the integration (can be set to a value smaller than t0 for backward integration)

Returns:

final state, its time will be the same as finalTime if integration reached its target, but may be different if some ODEEventHandler stops it at some point.

Throws:

MathIllegalArgumentException - if integration step is too small

MathIllegalStateException - if the number of functions evaluations is exceeded

getMinReduction

public double getMinReduction()

Get the minimal reduction factor for stepsize control.

Returns:

minimal reduction factor

setMinReduction

public void setMinReduction(double minReduction)

Set the minimal reduction factor for stepsize control.

Parameters:

minReduction - minimal reduction factor

getMaxGrowth

public double getMaxGrowth()

Get the maximal growth factor for stepsize control.

Returns:

maximal growth factor

setMaxGrowth

public void setMaxGrowth(double maxGrowth)

Set the maximal growth factor for stepsize control.

Parameters:

maxGrowth - maximal growth factor

estimateError

protected abstract double estimateError(double[][] yDotK,
                                        double[] y0,
                                        double[] y1,
                                        double h)

Compute the error ratio.

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