org.apache.commons.math3.ode.nonstiff
Class EulerIntegrator
java.lang.Object
org.apache.commons.math3.ode.AbstractIntegrator
org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator
org.apache.commons.math3.ode.nonstiff.EulerIntegrator
- All Implemented Interfaces:
- FirstOrderIntegrator, ODEIntegrator
public class EulerIntegrator
- extends RungeKuttaIntegrator
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.
- Since:
- 1.2
- Version:
- $Id: EulerIntegrator.java 3720 2012-03-16 16:34:17Z CardosoP $
- See Also:
MidpointIntegrator
,
ClassicalRungeKuttaIntegrator
,
GillIntegrator
,
ThreeEighthesIntegrator
Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator |
acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, sanityChecks, setEquations, setMaxEvaluations, setStateInitialized |
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
EulerIntegrator
public EulerIntegrator(double step)
- Simple constructor.
Build an Euler integrator with the given step.
- Parameters:
step
- integration step
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