org.opensourcephysics.numerics

Class EulerRichardson

java.lang.Object

org.opensourcephysics.numerics.AbstractODESolver

org.opensourcephysics.numerics.EulerRichardson

All Implemented Interfaces:

ODESolver

public class EulerRichardson
extends AbstractODESolver

An Euler-Richardson (midpoint) method ODE solver. The Euler-Richardson method uses the state at the beginning of the interval to estimate the state at the midpoint. x(midpoint) = x(n) + v(n)*dt/2 v(midpoint) = v(n) + a(n)*dt/2 t(midpoint) = t(n) + dt/2 The midpoint state is then used to calculate the final state.

Version:

1.0

Author:

Wolfgang Christian

Field Summary

Fields inherited from class org.opensourcephysics.numerics.AbstractODESolver

numEqn, ode, stepSize

Constructor Summary

Constructors

Constructor and Description
EulerRichardson(ODE ode) Constructs the EulerRichardson ODESolver for a system of ordinary differential equations.

Method Summary

Methods

Modifier and Type	Method and Description
void	initialize(double stepSize) Initializes the ODE solver.
double	step() Steps (advances) the differential equations by the stepSize.

Methods inherited from class org.opensourcephysics.numerics.AbstractODESolver

getStepSize, setStepSize

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

EulerRichardson

public EulerRichardson(ODE ode)

Constructs the EulerRichardson ODESolver for a system of ordinary differential equations.

Parameters:

ode - the system of differential equations.

Method Detail

initialize

public void initialize(double stepSize)

Initializes the ODE solver. The rate and midstate arrays are allocated. The number of differential equations is determined by invoking getState().length on the ODE.

Specified by:

initialize in interface ODESolver

Overrides:

initialize in class AbstractODESolver

Parameters:

stepSize -

step

public double step()

Steps (advances) the differential equations by the stepSize. The ODESolver invokes the ODE's getState method to obtain the initial state of the system. The ODESolver advances the solution and copies the new state into the state array at the end of the solution step.

Specified by:

step in interface ODESolver

Specified by:

step in class AbstractODESolver

Returns:

the step size