org.opensourcephysics.numerics
Class Verlet

java.lang.Object
  org.opensourcephysics.numerics.AbstractODESolver
      org.opensourcephysics.numerics.Verlet

All Implemented Interfaces:

ODESolver

public class Verlet
extends AbstractODESolver

Verlet: A velocity Verlet method ODE solver. The velocity Verlet algorithm is a self-starting equivalent of the Verlet algorithm. It assumes a constant acceleration to estimate the final position and an average accleration to estimate the final velocity. The position is first updated, the force is calcualted at the new position, and then the velocity is updated. x(n+1) = x(n) + v(n)* dt + a(n)*dt*dt/2 a_est=F(x(n+1),v(n),t)/m v(n+1) = v(n) + (a(n)+a_est)*dt/2 CAUTION! This implementation assumes that the state variables alternate between position and velocity with the last variable being time. That is, the state vector is ordered as follows: x1, d x1/dt, x2, d x2/dt, x3, d x3/dt ..... xN, d xN/dt, t

Version:

1.1

Author:

Wolfgang Christian

Field Summary

Fields inherited from class org.opensourcephysics.numerics.AbstractODESolver

numEqn, ode, stepSize

Constructor Summary

Verlet(ODE ode)
Constructs the velocity Verlet ODESolver for a system of ordinary differential equations.

Method Summary

int	getRateCounter() Gets the counter that records the number of times the rate has been evaluated during the current step.
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

Verlet

public Verlet(ODE ode)

Constructs the velocity Verlet 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 array is 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 -

getRateCounter

public int getRateCounter()

Gets the counter that records the number of times the rate has been evaluated during the current step. This method allows a model to improve its performance by enabling the model to determine if this is the first or second time that the rate is being evaluated. The Verlet algorithm first invokes the model's getRate method to update the position and then again to update velocity. Because the force at the new position is computed the second time that getRate is invoked, a model can improve its performance if it skips the force computation during the first call to getRate. A typical dynamics simulation should comptute the force when rateCounter is one and stores this force for use during the next postion update. The Verlet algorithm will perform correctly (but more slowly) if the force is computed every time that getRate is invoked.

Returns:

int the counter

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