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java.lang.Objectorg.apache.commons.math.ode.AbstractIntegrator
org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator
org.apache.commons.math.ode.nonstiff.EmbeddedRungeKuttaIntegrator
public abstract class EmbeddedRungeKuttaIntegrator
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.
Method Summary | |
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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 |
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getCurrentStepStart, getMaxStep, getMinStep, initializeStep, setInitialStepSize |
Methods inherited from class org.apache.commons.math.ode.AbstractIntegrator |
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addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, setMaxEvaluations |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Method Detail |
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public abstract int getOrder()
public double getSafety()
public void setSafety(double safety)
safety
- safety factorpublic double integrate(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y) throws DerivativeException, IntegratorException
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.
integrate
in interface FirstOrderIntegrator
integrate
in class AdaptiveStepsizeIntegrator
equations
- differential equations to integratet0
- initial timey0
- initial value of the state vector at t0t
- 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
EventHandler
stops it at some point.
DerivativeException
- this exception is propagated to the caller if
the underlying user function triggers one
IntegratorException
- if the integrator cannot perform integrationpublic double getMinReduction()
public void setMinReduction(double minReduction)
minReduction
- minimal reduction factorpublic double getMaxGrowth()
public void setMaxGrowth(double maxGrowth)
maxGrowth
- maximal growth factor
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