org.apache.commons.math3.ode.nonstiff

Class EmbeddedRungeKuttaFieldIntegrator<T extends RealFieldElement<T>>

java.lang.Object

org.apache.commons.math3.ode.AbstractFieldIntegrator<T>

org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator<T>

org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaFieldIntegrator<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FirstOrderFieldIntegrator<T>, FieldButcherArrayProvider<T>

Direct Known Subclasses:

DormandPrince54FieldIntegrator, DormandPrince853FieldIntegrator, HighamHall54FieldIntegrator

public abstract class EmbeddedRungeKuttaFieldIntegrator<T extends RealFieldElement<T>>
extends AdaptiveStepsizeFieldIntegrator<T>
implements FieldButcherArrayProvider<T>

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:

3.6

Method Summary

Modifier and Type	Method and Description
T	getMaxGrowth() Get the maximal growth factor for stepsize control.
T	getMinReduction() Get the minimal reduction factor for stepsize control.
abstract int	getOrder() Get the order of the method.
T	getSafety() Get the safety factor for stepsize control.
FieldODEStateAndDerivative<T>	integrate(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T finalTime) Integrate the differential equations up to the given time.
void	setMaxGrowth(T maxGrowth) Set the maximal growth factor for stepsize control.
void	setMinReduction(T minReduction) Set the minimal reduction factor for stepsize control.
void	setSafety(T safety) Set the safety factor for stepsize control.

Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator

getMaxStep, getMinStep, initializeStep, setInitialStepSize, setStepSizeControl, setStepSizeControl

Methods inherited from class org.apache.commons.math3.ode.AbstractFieldIntegrator

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

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider

getA, getB, getC

Method Detail

getOrder

public abstract int getOrder()

Get the order of the method.

Returns:

order of the method

getSafety

public T getSafety()

Get the safety factor for stepsize control.

Returns:

safety factor

setSafety

public void setSafety(T safety)

Set the safety factor for stepsize control.

Parameters:

safety - safety factor

integrate

public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations,
                                               FieldODEState<T> initialState,
                                               T finalTime)
                                        throws NumberIsTooSmallException,
                                               DimensionMismatchException,
                                               MaxCountExceededException,
                                               NoBracketingException

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 (FirstOrderFieldIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

Specified by:

integrate in interface FirstOrderFieldIntegrator<T extends RealFieldElement<T>>

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 FieldEventHandler stops it at some point.

Throws:

NumberIsTooSmallException - if integration step is too small

MaxCountExceededException - if the number of functions evaluations is exceeded

NoBracketingException - if the location of an event cannot be bracketed

DimensionMismatchException

getMinReduction

public T getMinReduction()

Get the minimal reduction factor for stepsize control.

Returns:

minimal reduction factor

setMinReduction

public void setMinReduction(T minReduction)

Set the minimal reduction factor for stepsize control.

Parameters:

minReduction - minimal reduction factor

getMaxGrowth

public T getMaxGrowth()

Get the maximal growth factor for stepsize control.

Returns:

maximal growth factor

setMaxGrowth

public void setMaxGrowth(T maxGrowth)

Set the maximal growth factor for stepsize control.

Parameters:

maxGrowth - maximal growth factor