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

java.lang.Object
  org.apache.commons.math3.ode.AbstractIntegrator
      org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator
          org.apache.commons.math3.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

Version:

$Id: EmbeddedRungeKuttaIntegrator.java 17623 2017-05-19 07:45:31Z bignon $

Field Summary

protected int[]

estimateError Array of states whose error has to be estimated.

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

protected	EmbeddedRungeKuttaIntegrator(String name, boolean fsal, double[] c, double[][] a, double[] b, org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Build a Runge-Kutta integrator with the given Butcher array.
protected	EmbeddedRungeKuttaIntegrator(String name, boolean fsal, double[] c, double[][] a, double[] b, org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Build a Runge-Kutta integrator with the given Butcher array.

Method Summary

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.
protected void	initIntegration(double t0, double[] y0, double t) Prepare the start of an integration.
void	integrate(ExpandableStatefulODE equations, double t) Integrate a set of 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.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, integrate, setEquations, setMaxEvaluations, setStateInitialized

Methods inherited from class java.lang.Object

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

Field Detail

estimateError

protected int[] estimateError

Array of states whose error has to be estimated.

Constructor Detail

EmbeddedRungeKuttaIntegrator

protected EmbeddedRungeKuttaIntegrator(String name,
                                       boolean fsal,
                                       double[] c,
                                       double[][] a,
                                       double[] b,
                                       org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype,
                                       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 - indicate that the method is an fsal

c - time steps from Butcher array (without the first zero)

a - internal weights from Butcher array (without the first empty row)

b - propagation weights for the high order method from Butcher array

prototype - prototype of the step interpolator to use

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,
                                       boolean fsal,
                                       double[] c,
                                       double[][] a,
                                       double[] b,
                                       org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype,
                                       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 - indicate that the method is an fsal

c - time steps from Butcher array (without the first zero)

a - internal weights from Butcher array (without the first empty row)

b - propagation weights for the high order method from Butcher array

prototype - prototype of the step interpolator to use

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

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 void integrate(ExpandableStatefulODE equations,
                      double t)
               throws NumberIsTooSmallException,
                      DimensionMismatchException,
                      MaxCountExceededException,
                      NoBracketingException

Integrate a set of differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

The set of differential equations is composed of a main set, which can be extended by some sets of secondary equations. The set of equations must be already set up with initial time and partial states. At integration completion, the final time and partial states will be available in the same object.

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

Specified by:

integrate in class AdaptiveStepsizeIntegrator

Parameters:

equations - complete set of differential equations to integrate

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

Throws:

NumberIsTooSmallException - if integration step is too small

DimensionMismatchException - if the dimension of the complete state does not match the complete equations sets dimension

MaxCountExceededException - if the number of functions evaluations is exceeded

NoBracketingException - if the location of an event cannot be bracketed

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

initIntegration

protected void initIntegration(double t0,
                               double[] y0,
                               double t)

Prepare the start of an integration.

Overrides:

initIntegration in class AbstractIntegrator

Parameters:

t0 - start value of the independent time variable

y0 - array containing the start value of the state vector

t - target time for the integration