public abstract class EmbeddedRungeKuttaIntegrator extends AdaptiveStepsizeIntegrator
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.
mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeToleranceisLastStep, resetOccurred, stepHandlers, stepSize, stepStart| Modifier | Constructor and Description |
|---|---|
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.
|
| Modifier and Type | Method and Description |
|---|---|
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.
|
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.
|
filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControlacceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCounter, getCurrentSignedStepsize, getEvaluations, getEvaluationsCounter, getEventHandlers, getExpandable, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, setEquations, setMaxEvaluations, setStateInitializedprotected 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)
name - name of the methodfsal - indicate that the method is an fsalc - 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 arrayprototype - prototype of the step interpolator to useminStep - minimal step (sign is irrelevant, regardless of
integration direction, forward or backward), the last step can
be smaller than thismaxStep - maximal step (sign is irrelevant, regardless of
integration direction, forward or backward), the last step can
be smaller than thisscalAbsoluteTolerance - allowed absolute errorscalRelativeTolerance - allowed relative errorprotected 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)
name - name of the methodfsal - indicate that the method is an fsalc - 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 arrayprototype - prototype of the step interpolator to useminStep - minimal step (must be positive even for backward
integration), the last step can be smaller than thismaxStep - maximal step (must be positive even for backward
integration)vecAbsoluteTolerance - allowed absolute errorvecRelativeTolerance - allowed relative errorpublic abstract int getOrder()
public double getSafety()
public void setSafety(double safety)
safety - safety factorpublic void integrate(ExpandableStatefulODE equations, double t) throws NumberIsTooSmallException, DimensionMismatchException, MaxCountExceededException, NoBracketingException
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.
integrate in class AdaptiveStepsizeIntegratorequations - complete set of differential equations to integratet - target time for the integration
(can be set to a value smaller than t0 for backward integration)NumberIsTooSmallException - if integration step is too smallDimensionMismatchException - if the dimension of the complete state does not
match the complete equations sets dimensionMaxCountExceededException - if the number of functions evaluations is exceededNoBracketingException - if the location of an event cannot be bracketedpublic double getMinReduction()
public void setMinReduction(double minReduction)
minReduction - minimal reduction factorpublic double getMaxGrowth()
public void setMaxGrowth(double maxGrowth)
maxGrowth - maximal growth factorprotected abstract double estimateError(double[][] yDotK,
double[] y0,
double[] y1,
double h)
yDotK - derivatives computed during the first stagesy0 - estimate of the step at the start of the stepy1 - estimate of the step at the end of the steph - current stepCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.