org.apache.commons.math3.ode.nonstiff
Class EulerIntegrator

java.lang.Object
  extended by org.apache.commons.math3.ode.AbstractIntegrator
      extended by org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator
          extended by 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 1416643 2012-12-03 19:37:14Z tn $
See Also:
MidpointIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, ThreeEighthesIntegrator

Field Summary
 
Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator
isLastStep, resetOccurred, stepHandlers, stepSize, stepStart
 
Constructor Summary
EulerIntegrator(double step)
          Simple constructor.
 
Method Summary
 
Methods inherited from class org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator
integrate
 
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
 

Constructor Detail

EulerIntegrator

public EulerIntegrator(double step)
Simple constructor. Build an Euler integrator with the given step.

Parameters:
step - integration step


Copyright © 2003-2012 The Apache Software Foundation. All Rights Reserved.