org.apache.commons.math.ode.nonstiff

Class EmbeddedRungeKuttaIntegrator

java.lang.Object

org.apache.commons.math.ode.AbstractIntegrator

org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator

org.apache.commons.math.ode.nonstiff.EmbeddedRungeKuttaIntegrator

All Implemented Interfaces:

FirstOrderIntegrator, ODEIntegrator

Direct Known Subclasses:

DormandPrince54Integrator, DormandPrince853Integrator, HighamHall54Integrator

public abstract class EmbeddedRungeKuttaIntegrator
extends AdaptiveStepsizeIntegrator

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.

Since:

1.2

Method Summary

Modifier and Type	Method and Description
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.
double	integrate(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y) 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.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator

getCurrentStepStart, getMaxStep, getMinStep, initializeStep, setInitialStepSize

Methods inherited from class org.apache.commons.math.ode.AbstractIntegrator

addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, setMaxEvaluations

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

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 double integrate(FirstOrderDifferentialEquations equations,
                        double t0,
                        double[] y0,
                        double t,
                        double[] y)
                 throws DerivativeException,
                        IntegratorException

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 FirstOrderIntegrator

Specified by:

integrate in class AdaptiveStepsizeIntegrator

Parameters:

equations - differential equations to integrate

t0 - initial time

y0 - initial value of the state vector at t0

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

y - placeholder where to put the state vector at each successful step (and hence at the end of integration), can be the same object as y0

Returns:

stop time, will be the same as target time if integration reached its target, but may be different if some EventHandler stops it at some point.

Throws:

DerivativeException - this exception is propagated to the caller if the underlying user function triggers one

IntegratorException - if the integrator cannot perform integration

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