com.imsl.math
Class OdeRungeKutta

java.lang.Object
  com.imsl.math.OdeRungeKutta

All Implemented Interfaces:

Serializable, Cloneable

public class OdeRungeKutta
extends Object
implements Serializable, Cloneable

Solves an initial-value problem for ordinary differential equations using the Runge-Kutta-Verner fifth-order and sixth-order method.

Class OdeRungeKutta finds an approximation to the solution of a system of first-order differential equations of the form with given initial data. The routine attempts to keep the global error proportional to a user-specified tolerance. This routine is efficient for nonstiff systems where the derivative evaluations are not expensive.

OdeRungeKutta is based on a code designed by Hull, Enright and Jackson (1976, 1977). It uses Runge-Kutta formulas of order five and six developed by J. H. Verner.

See Also:

Example, Serialized Form

Nested Class Summary

static class	OdeRungeKutta.DidNotConvergeException The iteration did not converge.
static interface	OdeRungeKutta.Function Public interface for user supplied function to OdeRungeKutta object.
static class	OdeRungeKutta.ToleranceTooSmallException Tolerance is too small.

Field Summary

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

Constructor Summary

OdeRungeKutta(OdeRungeKutta.Function function)
Constructs an ODE solver to solve the initial value problem dy/dx = f(x,y)

Method Summary

protected void	examineStep(int state, double x, double[] y) Called before and after each internal step.
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.
void	solve(double x, double xEnd, double[] y) Integrates the ODE system from x to xEnd.
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

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

BEFORE_STEP

public static final int BEFORE_STEP

Used by method examineStep to indicate examining before the next step

See Also:

Constant Field Values

Constructor Detail

OdeRungeKutta

public OdeRungeKutta(OdeRungeKutta.Function function)

Constructs an ODE solver to solve the initial value problem dy/dx = f(x,y)

Parameters:

function - Implementation of interface Function that defines the right-hand side function f(x,y)

Method Detail

examineStep

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

Called before and after each internal step.

Parameters:

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

x - double representing the indepenent variable.

y - double array containing the dependent variables.

setFloor

public void setFloor(double floor)

Sets the value used in the norm computation.

Parameters:

floor - double used in the norm computation, default value is 1.

Throws:

IllegalArgumentException - is thrown if floor is less than or equal to zero.

setInitialStepsize

public void setInitialStepsize(double stepsize)

Sets the initial internal step size.

Parameters:

stepsize - double specifying the initial internal step size.

Throws:

IllegalArgumentException - is thrown if stepsize is less than or equal to zero.

setMaximumStepsize

public void setMaximumStepsize(double stepsize)

Sets the maximum internal step size.

Parameters:

stepsize - Maximum internal step size. Default value is 2.

Throws:

IllegalArgumentException - is thrown if stepsize is less than or equal to 0.

setMaxSteps

public void setMaxSteps(int maxSteps)

Sets the maximum number of internal steps allowed.

Parameters:

maxSteps - int specifying the maximum number of internal steps allowed, default value is 500

Throws:

IllegalArgumentException - is thrown if maxSteps is less than or equal to zero.

setMinimumStepsize

public void setMinimumStepsize(double stepsize)

Sets the minimum internal step size.

Parameters:

stepsize - Minimum internal step size. Default value is 0.

Throws:

IllegalArgumentException - is thrown if stepsize is less than or equal to 0.

setNorm

public void setNorm(int normMethod)

Sets the switch for determining the error norm.

Parameters:

normMethod - int specifying the switch for determining the error norm, default value is 0. In the following, is the absolute value fo an estimate of the error in

norm	Constraint
0	Minimum of the absolute error and the relative error, equals the maximum of
1	Absolute error, equals
2	Maximum of

Throws:

IllegalArgumentException - is thrown if norm is is not 0, 1, or 2.

setScale

public void setScale(double scale)

Sets the scaling factor.

Parameters:

scale - double specifying the scaling factor, default value is 1.e0

Throws:

IllegalArgumentException - is thrown if scale is less than or equal to 0.

setTolerance

public void setTolerance(double tolerance)

Sets the error tolerance.

Parameters:

tolerance - double specifying the error tolerance. Default value is 1.0e-6.

Throws:

IllegalArgumentException - is thrown if tolerance less than or equal 0.

solve

public void solve(double x,
                  double xEnd,
                  double[] y)
           throws OdeRungeKutta.ToleranceTooSmallException,
                  OdeRungeKutta.DidNotConvergeException

Integrates the ODE system from x to xEnd. On all but the first call to solve, the value of x must equal the value of xEnd for the previous call.

Parameters:

x - double specifying the independent variable

xEnd - double specifying the value of x at which the solution is desired

y - On input, double array containing the initial values. On output, double array containing the approximate solution.

Throws:

OdeRungeKutta.DidNotConvergeException - is thrown if the number of internal steps exceeds maxSteps (default 500). This can be an indication that the ODE system is stiff. This exception can also be thrown if the error tolerance condition could not be met.

OdeRungeKutta.ToleranceTooSmallException - is thrown if the computation does not converge on some step.

vnorm

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

Returns the norm of a vector.

Parameters:

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

y - double array containing the values of the dependent variable

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

Returns:

double scalar value representing the norm of the vector v