com.imsl.math

Class ODE

java.lang.Object

com.imsl.math.ODE

All Implemented Interfaces:

Serializable, Cloneable

Direct Known Subclasses:

OdeAdamsGear, OdeRungeKutta

public abstract class ODE
extends Object
implements Serializable, Cloneable

ODE represents and solves an initial-value problem for ordinary differential equations.

See Also:

Runge-Kutta Example, Adams-Gear Example, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static int	AFTER_SUCCESSFUL_STEP Used by method examineStep to indicate examining after a successful step
static int	AFTER_UNSUCCESSFUL_STEP Used by method examineStep to indicate examining after an unsuccessful step
static int	BEFORE_STEP Used by method examineStep to indicate examining before the next step
static int	ERROR_NORM_ABS Used by method setNorm to indicate that the error norm to be used is to be the absolute error, equals \(max(|e_i|)\)
static int	ERROR_NORM_EUCLIDEAN Used by method setNorm to indicate that the error norm to be used is to be the scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations
static int	ERROR_NORM_MAX Used by method setNorm to indicate that the error norm to be used is to be the maximum of \(e_i/max(|y_i(t)|, floor)\) where floor is set via setFloor
static int	ERROR_NORM_MINABSREL Used by method setNorm to indicate that the error norm to be used is to be the minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)

Constructor Summary

Constructors

Constructor and Description
ODE()

Method Summary

Modifier and Type	Method and Description
protected void	examineStep(int state, double t, double[] y) Called before and after each internal step.
double	getFloor() Returns the value used in the norm computation.
double	getInitialStepsize() Returns the initial internal step size.
double	getMaximumStepsize() Returns the maximum internal step size.
int	getMaxSteps() Returns the maximum number of internal steps allowed.
double	getMinimumStepsize() Returns the minimum internal step size.
int	getNorm() Returns the switch for determining the error norm.
double	getScale() Returns the scaling factor.
double	getTolerance() Returns the error tolerance.
void	setFloor(double floor) Sets the value used in the norm computation.
void	setInitialStepsize(double stepsize) Sets the initial internal step size.
void	setMaximumStepsize(double stepsize) Sets the maximum internal step size.
void	setMaxSteps(int maxSteps) Sets the maximum number of internal steps allowed.
void	setMinimumStepsize(double stepsize) Sets the minimum internal step size.
void	setNorm(int normMethod) Sets the switch for determining the error norm.
void	setScale(double scale) Sets the scaling factor.
void	setTolerance(double tolerance) Sets the error tolerance.
protected double	vnorm(double[] v, double[] y, double[] ymax) Returns the norm of a vector.

Methods inherited from class java.lang.Object

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

Field Detail

BEFORE_STEP

public static final int BEFORE_STEP

Used by method examineStep to indicate examining before the next step

See Also:

Constant Field Values

AFTER_SUCCESSFUL_STEP

public static final int AFTER_SUCCESSFUL_STEP

Used by method examineStep to indicate examining after a successful step

See Also:

Constant Field Values

AFTER_UNSUCCESSFUL_STEP

public static final int AFTER_UNSUCCESSFUL_STEP

Used by method examineStep to indicate examining after an unsuccessful step

See Also:

Constant Field Values

ERROR_NORM_MINABSREL

public static final int ERROR_NORM_MINABSREL

Used by method setNorm to indicate that the error norm to be used is to be the minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)

See Also:

Constant Field Values

ERROR_NORM_ABS

public static final int ERROR_NORM_ABS

Used by method setNorm to indicate that the error norm to be used is to be the absolute error, equals \(max(|e_i|)\)

See Also:

Constant Field Values

ERROR_NORM_MAX

public static final int ERROR_NORM_MAX

Used by method setNorm to indicate that the error norm to be used is to be the maximum of \(e_i/max(|y_i(t)|, floor)\) where floor is set via setFloor

See Also:

Constant Field Values

ERROR_NORM_EUCLIDEAN

public static final int ERROR_NORM_EUCLIDEAN

Used by method setNorm to indicate that the error norm to be used is to be the scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations

See Also:

Constant Field Values

Constructor Detail

ODE

public ODE()

Method Detail

examineStep

protected void examineStep(int state,
                           double t,
                           double[] y)

Called before and after each internal step. This method can be over-ridden by the user to examine intermediate values of t and y.

Parameters:

state - an int, one of BEFORE_STEP, AFTER_SUCCESSFUL_STEP or AFTER_UNSUCCESSFUL_STEP.

t - double representing the independent variable.

y - double array containing the dependent variables.

setFloor

public void setFloor(double floor)

Sets the value used in the norm computation.

Parameters:

floor - a double used in the norm computation. floor must be greater than zero.
Default: floor = 1.0

setInitialStepsize

public void setInitialStepsize(double stepsize)

Sets the initial internal step size.

Parameters:

stepsize - a double specifying the initial internal step size. stepsize must be greater than or equal to zero. Default: stepsize = 0.0

setMaximumStepsize

public void setMaximumStepsize(double stepsize)

Sets the maximum internal step size.

Parameters:

stepsize - a double specifying the maximum internal step size. stepsize must be greater than zero.
Default: See the setMaximumStepsize method in the subclasses for the default values used.

setMaxSteps

public void setMaxSteps(int maxSteps)

Sets the maximum number of internal steps allowed.

Parameters:

maxSteps - an int specifying the maximum number of internal steps allowed. maxSteps must be greater than zero. Default: maxSteps = 500

setMinimumStepsize

public void setMinimumStepsize(double stepsize)

Sets the minimum internal step size.

Parameters:

stepsize - a double specifying the minimum internal step size. stepsize must be greater than or equal to zero. Default: stepsize = 0.0

setNorm

public void setNorm(int normMethod)

Sets the switch for determining the error norm.

Parameters:

normMethod - an int specifying the switch for determining the error norm.
Default: normMethod = ERROR_NORM_MINABSREL
In the following table, \(e_i\) is the absolute value for an estimate of the error in \(y_i(t)\).

normMethod	Constraint
ERROR_NORM_MINABSREL	Minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)
ERROR_NORM_ABS	Absolute error, equals \(max(e_i)\)
ERROR_NORM_MAX	Maximum of \(e_i/max(|y_i(t)|, floor)\)
ERROR_NORM_EUCLIDEAN	Scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations

setScale

public void setScale(double scale)

Sets the scaling factor.

Parameters:

scale - a double specifying the scaling factor. scale must be greater than zero.
Default: scale = 1.0

setTolerance

public void setTolerance(double tolerance)

Sets the error tolerance.

Parameters:

tolerance - a double specifying the error tolerance. tolerance must be greater than zero. Default: tolerance = 1.0e-6

getTolerance

public double getTolerance()

Returns the error tolerance.

Returns:

a double specifying the error tolerance.

getInitialStepsize

public double getInitialStepsize()

Returns the initial internal step size.

Returns:

a double specifying the initial internal step size.

getMinimumStepsize

public double getMinimumStepsize()

Returns the minimum internal step size.

Returns:

a double specifying the minimum internal step size.

getMaximumStepsize

public double getMaximumStepsize()

Returns the maximum internal step size.

Returns:

a double specifying the maximum internal step size.

getScale

public double getScale()

Returns the scaling factor.

Returns:

a double specifying the scaling factor.

getNorm

public int getNorm()

Returns the switch for determining the error norm.

Returns:

an int specifying the switch for determining the error norm. In the following, \(e_i\) is the absolute value for an estimate of the error in \(y_i(t)\).

normMethod	Constraint
ERROR_NORM_MINABSREL	Minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)
ERROR_NORM_ABS	Absolute error, equals \(max(e_i)\)
ERROR_NORM_MAX	Maximum of \(e_i/max(|y_i(t)|, floor)\)
ERROR_NORM_EUCLIDEAN	Scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations

getFloor

public double getFloor()

Returns the value used in the norm computation.

Returns:

a double used in the norm computation.

getMaxSteps

public int getMaxSteps()

Returns the maximum number of internal steps allowed.

Returns:

an int specifying the maximum number of internal steps allowed.

vnorm

protected double vnorm(double[] v,
                       double[] y,
                       double[] ymax)

Returns the norm of a vector. This method can be over-ridden by the user to supply a different norm than those available through setNorm.

Parameters:

v - a double array containing the vector whose norm is to be computed

y - a double array containing the values of the dependent variable

ymax - a double array containing the maximum y values computed thus far

Returns:

a double scalar value representing the norm of the vector v