org.apache.commons.math.ode
Class EulerIntegrator

java.lang.Object
  extended by org.apache.commons.math.ode.RungeKuttaIntegrator
      extended by org.apache.commons.math.ode.EulerIntegrator
All Implemented Interfaces:
FirstOrderIntegrator

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:
$Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
See Also:
MidpointIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, ThreeEighthesIntegrator

Field Summary
private static double[][] a
          Internal weights Butcher array.
private static double[] b
          Propagation weights Butcher array.
private static double[] c
          Time steps Butcher array.
private static java.lang.String methodName
          Integrator method name.
 
Fields inherited from class org.apache.commons.math.ode.RungeKuttaIntegrator
switchesHandler
 
Constructor Summary
EulerIntegrator(double step)
          Simple constructor.
 
Method Summary
 java.lang.String getName()
          Get the name of the method.
 
Methods inherited from class org.apache.commons.math.ode.RungeKuttaIntegrator
addSwitchingFunction, getCurrentSignedStepsize, getCurrentStepStart, getStepHandler, integrate, setStepHandler
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

methodName

private static final java.lang.String methodName
Integrator method name.

See Also:
Constant Field Values

c

private static final double[] c
Time steps Butcher array.


a

private static final double[][] a
Internal weights Butcher array.


b

private static final double[] b
Propagation weights Butcher array.

Constructor Detail

EulerIntegrator

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

Parameters:
step - integration step
Method Detail

getName

public java.lang.String getName()
Get the name of the method.

Specified by:
getName in interface FirstOrderIntegrator
Specified by:
getName in class RungeKuttaIntegrator
Returns:
name of the method