org.apache.commons.math3.ode.nonstiff

Class 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:
$Id: EulerIntegrator.java 1588755 2014-04-20 13:30:16Z luc$