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 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