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java.lang.Objectorg.apache.commons.math.ode.AbstractIntegrator
org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator
org.apache.commons.math.ode.MultistepIntegrator
public abstract class MultistepIntegrator
This class is the base class for multistep integrators for Ordinary Differential Equations.
We define scaled derivatives si(n) at step n as:
s1(n) = h y'n for first derivative s2(n) = h2/2 y''n for second derivative s3(n) = h3/6 y'''n for third derivative ... sk(n) = hk/k! y(k)n for kth derivative
Rather than storing several previous steps separately, this implementation uses the Nordsieck vector with higher degrees scaled derivatives all taken at the same step (yn, s1(n) and rn) where rn is defined as:
rn = [ s2(n), s3(n) ... sk(n) ]T(we omit the k index in the notation for clarity)
Multistep integrators with Nordsieck representation are highly sensitive to large step changes because when the step is multiplied by a factor a, the kth component of the Nordsieck vector is multiplied by ak and the last components are the least accurate ones. The default max growth factor is therefore set to a quite low value: 21/order.
AdamsBashforthIntegrator
,
AdamsMoultonIntegrator
Nested Class Summary | |
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static interface |
MultistepIntegrator.NordsieckTransformer
Transformer used to convert the first step to Nordsieck representation. |
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. |
double |
getSafety()
Get the safety factor for stepsize control. |
ODEIntegrator |
getStarterIntegrator()
Get the starter integrator. |
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. |
void |
setStarterIntegrator(FirstOrderIntegrator starterIntegrator)
Set the starter integrator. |
Methods inherited from class org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator |
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getCurrentStepStart, getMaxStep, getMinStep, initializeStep, integrate, 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 ODEIntegrator getStarterIntegrator()
public void setStarterIntegrator(FirstOrderIntegrator starterIntegrator)
The various step and event handlers for this starter integrator will be managed automatically by the multi-step integrator. Any user configuration for these elements will be cleared before use.
starterIntegrator
- starter integratorpublic double getMinReduction()
public void setMinReduction(double minReduction)
minReduction
- minimal reduction factorpublic double getMaxGrowth()
public void setMaxGrowth(double maxGrowth)
maxGrowth
- maximal growth factorpublic double getSafety()
public void setSafety(double safety)
safety
- safety factor
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