org.opensourcephysics.numerics.rk
Class Radau5

java.lang.Object
  org.opensourcephysics.numerics.rk.irk.Radau5Light
      org.opensourcephysics.numerics.rk.irk.Radau5Adaptive
          org.opensourcephysics.numerics.rk.Radau5

All Implemented Interfaces:

ODESolverInterpolator

public class Radau5
extends Radau5Adaptive
implements ODESolverInterpolator

Title: Radau5 Description: 5th order implicit RK Radau solver

Version:

1.0 January 2009

Author:

Francisco Esquembre (based on code by Andrei Goussev / based on Fortran code by E. Hairer and G. Wanner)

Constructor Summary

Radau5(ODE ode)

Method Summary

double[]	bestInterpolate(double _time, double[] _state) Similar to interpolate(), but using the best estimate the algorith can provide and only between the current time and getMaximumTime().
double[]	getCurrentRate() Returns the rate of the current state
double	getInternalStepSize() Returns the actual internal step size
double	getMaximumTime() Returns the maximum time forward in time (or minimum, if the step is negative) for which the solver can interpolate without doing any internal step.
StateMemory	getStateMemory() Provides access to the internal StateMemory responsible for interpolations.
double	internalStep() Steps the internal step as much as possible (respecting the step size and the tolerance, if any).
double[]	interpolate(double _time, boolean useLeftApproximation, double[] _state) Implements continuous vector function that approximates the solution of the ODE.
double[]	interpolate(double _time, boolean _useLeftApproximation, double[] _state, int _beginIndex, int _length)
double	interpolate(double _time, boolean _useLeftApproximation, int _index)
void	reinitialize(double[] _state) Does the minimum (soft) initialization of the solver to a given state.
void	setEstimateFirstStep(boolean _estimate) Makes adaptive steps estimate the best initial step after reinitialize().
void	setMemoryLength(double length) Sets the length of the memory requested to the solver.

Methods inherited from class org.opensourcephysics.numerics.rk.irk.Radau5Adaptive

doStep, getErrorCode, setTolerances

Methods inherited from class org.opensourcephysics.numerics.rk.irk.Radau5Light

getCounter, getODE, getStepSize, initialize, setMaximumStepSize, setStepSize

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.opensourcephysics.numerics.ODESolverInterpolator

getCounter, getODE, getStepSize, initialize, setMaximumStepSize, setStepSize, setTolerances

Constructor Detail

Radau5

public Radau5(ODE ode)

Method Detail

reinitialize

public void reinitialize(double[] _state)

Description copied from interface: ODESolverInterpolator

Does the minimum (soft) initialization of the solver to a given state. The memory is preserved. Users of an ODESolverInterpolator MUST call reinitialize (or the harder initialize) whenever they change the state. Typically, solvers synchronize their internal states and auxiliary variables using the provided state.

Specified by:

reinitialize in interface ODESolverInterpolator

Overrides:

reinitialize in class Radau5Adaptive

Parameters:

_state - double[]

getCurrentRate

public double[] getCurrentRate()

Description copied from interface: ODESolverInterpolator

Returns the rate of the current state

Specified by:

getCurrentRate in interface ODESolverInterpolator

Returns:

setEstimateFirstStep

public final void setEstimateFirstStep(boolean _estimate)

Description copied from interface: ODESolverInterpolator

Makes adaptive steps estimate the best initial step after reinitialize(). If false, the given initial step (as set by setStepSize()) is used.

Specified by:

setEstimateFirstStep in interface ODESolverInterpolator

getMaximumTime

public final double getMaximumTime()

Description copied from interface: ODESolverInterpolator

Returns the maximum time forward in time (or minimum, if the step is negative) for which the solver can interpolate without doing any internal step.

Specified by:

getMaximumTime in interface ODESolverInterpolator

Returns:

double The maximum advance time or NaN if there was any error.

internalStep

public final double internalStep()

Description copied from interface: ODESolverInterpolator

Steps the internal step as much as possible (respecting the step size and the tolerance, if any).

Specified by:

internalStep in interface ODESolverInterpolator

Returns:

double Same as getMaximumTime()

getInternalStepSize

public double getInternalStepSize()

Description copied from interface: ODESolverInterpolator

Returns the actual internal step size

Specified by:

getInternalStepSize in interface ODESolverInterpolator

Returns:

setMemoryLength

public void setMemoryLength(double length)

Description copied from interface: ODESolverInterpolator

Sets the length of the memory requested to the solver. Must be a positive value. The user will then be able to ask for values of the state as far as the current time minus this length. 0 is the default for plain ODE, getMaximumDelay() is the minimum used by DDEs. Setting a value of Infinity makes the solver to remmeber for ever (i.e. as much as computer memory permits)

Specified by:

setMemoryLength in interface ODESolverInterpolator

getStateMemory

public StateMemory getStateMemory()

Description copied from interface: ODESolverInterpolator

Provides access to the internal StateMemory responsible for interpolations.

Specified by:

getStateMemory in interface ODESolverInterpolator

Returns:

interpolate

public double[] interpolate(double _time,
                            boolean useLeftApproximation,
                            double[] _state)

Implements continuous vector function that approximates the solution of the ODE. Value of the vector function constructs using interpolation coefficients

Specified by:

interpolate in interface ODESolverInterpolator

Parameters:

time - the point where approximation to the solution to be obtained. (0 < time < takenstepSize corresponds to the interpolation, in other cases output will indeed the extrapolation)

result - the result, i.e. approximated solution of ODE

Returns:

The state provided as argument or null if there is no interpolation available at this time.

interpolate

public double[] interpolate(double _time,
                            boolean _useLeftApproximation,
                            double[] _state,
                            int _beginIndex,
                            int _length)

interpolate

public double interpolate(double _time,
                          boolean _useLeftApproximation,
                          int _index)

bestInterpolate

public double[] bestInterpolate(double _time,
                                double[] _state)

Description copied from interface: ODESolverInterpolator

Similar to interpolate(), but using the best estimate the algorith can provide and only between the current time and getMaximumTime(). In some RK schemes, this results in computing the RK algorithm from the initial point. Therefore, this method typically involves a bigger computational load.

Specified by:

bestInterpolate in interface ODESolverInterpolator

Returns:

The state provided as argument or null if there was any previous error.