core.math
Class RungeKuttaErrorIntegration

java.lang.Object
  core.math.RungeKuttaErrorIntegration

public class RungeKuttaErrorIntegration

extends java.lang.Object

RungeKutta Integration with error analysis

Field Summary

(package private) int	dim
private double	eps
private VecTimeField	field
private double	hmin
(package private) double	maxStep
(package private) boolean	stepped
private Vec	xinput

Constructor Summary

RungeKuttaErrorIntegration()

RungeKuttaErrorIntegration(double maxStep)

Method Summary

Vec	ComputeStep(double s, double ds, int dim)
void	Evolve(VecTimeField field, Vec xinput, double s, double ds, double eps, double hmin)
static Vec	rungeKuttaFourthOrder(VecTimeField field, Vec X_at_s, Vec dXds_at_s, double s_start, double h, int dim) This is the basic fourth order RungeKutta stepping routine.
static double[]	rungeKuttaQualityControl(VecTimeField field, Vec Xnew, Vec dXds, double sgiven, double htry, double eps, Vec Xscal, int dim) Given a value of X and dX/ds at s, a stepsize h, an allowed error, and a way to compute dX/ds at new points, this method will return a new value of the dependent variables X at s, where s incremented over s by an amount not more than h, but perhaps much less than h, but with an error in X of less than the desired error.
void	SetStep(double maxStep)

Methods inherited from class java.lang.Object

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

Field Detail

stepped

boolean stepped

maxStep

double maxStep

dim

int dim

xinput

private Vec xinput

field

private VecTimeField field

eps

private double eps

hmin

private double hmin

Constructor Detail

RungeKuttaErrorIntegration

public RungeKuttaErrorIntegration()

RungeKuttaErrorIntegration

public RungeKuttaErrorIntegration(double maxStep)

Method Detail

SetStep

public void SetStep(double maxStep)

ComputeStep

public Vec ComputeStep(double s,
                       double ds,
                       int dim)

Evolve

public void Evolve(VecTimeField field,
                   Vec xinput,
                   double s,
                   double ds,
                   double eps,
                   double hmin)

rungeKuttaQualityControl

public static double[] rungeKuttaQualityControl(VecTimeField field,
                                                Vec Xnew,
                                                Vec dXds,
                                                double sgiven,
                                                double htry,
                                                double eps,
                                                Vec Xscal,
                                                int dim)

Given a value of X and dX/ds at s, a stepsize h, an allowed error, and a way to compute dX/ds at new points, this method will return a new value of the dependent variables X at s, where s incremented over s by an amount not more than h, but perhaps much less than h, but with an error in X of less than the desired error. The size of the step actually taken is hdid. If we are taking too small a step for the error we desire, we return hnext as an estimate of the step size for the next step which will still be just within our desired error.

Parameters:

Xnew - This is the valve of X at s

dXds - The derivative dX/ds at out initial value of the independent parameter.

sgiven - This is the initial value of the independent variable.

htry - The initial value of the stepsize to try, which is subsequently modified depending on the estimated error and our desired error.

eps - Desired error.

Xscal - Defines the meaning of error.

Returns:

The new value the dependent values, with other things stored in array, e.g. the new s, hdid, hnext, and so on

rungeKuttaFourthOrder

public static Vec rungeKuttaFourthOrder(VecTimeField field,
                                        Vec X_at_s,
                                        Vec dXds_at_s,
                                        double s_start,
                                        double h,
                                        int dim)

This is the basic fourth order RungeKutta stepping routine. Given the value X of the dependent variables at s, and a step size h, and the ability to evaluate the derivatives dX/ds at any s, the routine returns an estimate of the value of X at s + h.

Parameters:

X_at_s - This is the initial value of X at the starting value of s.

dXds_at_s - This is the initial value of the derivatives dX/ds at the starting value of s. This derivative must be provided to the routine.

s_start - The initial value of the independent variable.

h - The step size.

Returns:

An estimate of the value of the dependent variables X at s + h.