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java.lang.Objectorg.apache.commons.math3.ode.AbstractIntegrator
org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator
org.apache.commons.math3.ode.nonstiff.EulerIntegrator
public class EulerIntegrator
This class implements a simple Euler integrator for Ordinary Differential Equations.
The Euler algorithm is the simplest one that can be used to
integrate ordinary differential equations. It is a simple inversion
of the forward difference expression :
f'=(f(t+h)-f(t))/h
which leads to
f(t+h)=f(t)+hf'
. The interpolation scheme used for
dense output is the linear scheme already used for integration.
This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.
This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.
MidpointIntegrator
,
ClassicalRungeKuttaIntegrator
,
GillIntegrator
,
ThreeEighthesIntegrator
Field Summary | |
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private static double[][] |
STATIC_A
Internal weights Butcher array. |
private static double[] |
STATIC_B
Propagation weights Butcher array. |
private static double[] |
STATIC_C
Time steps Butcher array. |
Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator |
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isLastStep, resetOccurred, stepHandlers, stepSize, stepStart |
Constructor Summary | |
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EulerIntegrator(double step)
Simple constructor. |
Method Summary |
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Methods inherited from class org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator |
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integrate |
Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator |
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acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEvaluations, getEvaluationsCounter, getEventHandlers, getExpandable, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, sanityChecks, setEquations, setMaxEvaluations, setStateInitialized |
Methods inherited from class java.lang.Object |
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
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private static final double[] STATIC_C
private static final double[][] STATIC_A
private static final double[] STATIC_B
Constructor Detail |
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public EulerIntegrator(double step)
step
- integration step
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