integrators
Class AdamsIntegrator

java.lang.Object
  integrators.Integrator
      integrators.AdamsIntegrator

public class AdamsIntegrator

extends Integrator

Fourth-order Adams-Bashforth-Moulton predictor-corrector method, using coefficients given in Melvin Maron, Numerical Analysis: A Practical Approach c. 1982, p. 354-7. This Integrator uses fourth-order Runge-Kutta steps to start off the integration, or to restart it internally if the error compensation gets overwhelmed, and then computes a prediction of y(t+1) based on an Adams-Bashforth formula involving the derivatives at the present time and at three equally-spaced previous time points. It then uses the prediction to compute an estimate of the derivative at y(t+1), and computes another estimate of y(t+1) based on the Adams-Moulton formula involving the estimated derivatives at y(t-2), y(t-1), y(t), and y(t+1). The difference between the predicted y(t+1) and the corrected y(t+1) is used to compute an error estimate. Then the corrected y(t+1) is substituted into the system for another application of the Adams-Moulton formula, and the error estimate becomes the difference between the first corrected y(t+1) and the second. If the error is increasing, or if it is greater than the error tolerance, then the method assumes it took too big a step and tries to cut it in half using an interpolation between the stored derivative values. If this does not improve matters, Runge-Kutta steps are used re-stock the derivative array. Otherwise, if the error is tolerable, the timestep may be doubled. The method uses counters to make sure that the method doesn't increase the timestep too frequently or try to cut it by interpolation more than once before resorting to Runge-Kutta steps.

Nested Class Summary

Nested classes inherited from class integrators.Integrator

Integrator.NVmatrix, Integrator.NVvector

Constructor Summary

AdamsIntegrator()

Method Summary

void	init(Model model) Any object planning to use an Integrator of any kind MUST call its init(Model) method, which (among other things) is generally used to allocate storage arrays for the intermediates in an integration method.
float	IntegrateOneStep() Integrates across a single time step.
void	reset() Should be called after the Integrator has crossed an entire interval.

Methods inherited from class integrators.Integrator

copyNVarray, getCurrentValues, getDerivatives, getErrorEstimate, isType, setDefaultStepSize, setErrorTolerance, setFinalValues, setIntegrationValues, setStepSize

Methods inherited from class java.lang.Object

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

Constructor Detail

AdamsIntegrator

public AdamsIntegrator()

Method Detail

init

public void init(Model model)

Description copied from class: Integrator

Any object planning to use an Integrator of any kind MUST call its init(Model) method, which (among other things) is generally used to allocate storage arrays for the intermediates in an integration method. This method does NOT do any numerics so does not depend on the state of the model, but it DOES need to be called after the model has been properly populated with Cells and Nodes, and needs to be called again if these change.

Overrides:

init in class Integrator

reset

public void reset()

Description copied from class: Integrator

Should be called after the Integrator has crossed an entire interval. The base class does nothing; typical subclasses will override Integrator.reset() to reset the time step size to the default value. This method is NOT used to reallocate storage; that requires a call to init().

Overrides:

reset in class Integrator

IntegrateOneStep

public float IntegrateOneStep()

Description copied from class: Integrator

Integrates across a single time step. Return value is the size of the timestep, which may differ from that specified by the calling method if the Integrator subclass adapts the step size to match error requirements.

Overrides:

IntegrateOneStep in class Integrator