Package com.imsl.math

Class OdeRungeKutta

java.lang.Object

com.imsl.math.ODE

com.imsl.math.OdeRungeKutta

All Implemented Interfaces:

Serializable, Cloneable

public class OdeRungeKutta
extends ODE

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 \(\frac{dy}{dt} = y' = f(t,y)\) with given initial data. The class attempts to keep the global error proportional to a user-specified tolerance. This class 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

Nested Classes

Modifier and Type	Class	Description
static class	OdeRungeKutta.DidNotConvergeException	The iteration did not converge within the maximum number of steps allowed (default 500).
static interface	OdeRungeKutta.Function	Public interface for user supplied function to OdeRungeKutta object.
static class	OdeRungeKutta.ToleranceTooSmallException	Tolerance is too small or the problem is stiff.

Field Summary

Fields inherited from class com.imsl.math.ODE

AFTER_SUCCESSFUL_STEP, AFTER_UNSUCCESSFUL_STEP, BEFORE_STEP, ERROR_NORM_ABS, ERROR_NORM_EUCLIDEAN, ERROR_NORM_MAX, ERROR_NORM_MINABSREL

Constructor Summary

Constructors

Constructor	Description
OdeRungeKutta(OdeRungeKutta.Function function)	Constructs an ODE solver to solve the initial value problem dy/dt = f(t,y)

Method Summary

Modifier and Type	Method	Description
void	setMaximumStepsize(double stepsize)	Sets the maximum internal step size.
void	solve(double t, double tEnd, double[] y)	Integrates the ODE system from t to tEnd.

Methods inherited from class com.imsl.math.ODE

examineStep, getFloor, getInitialStepsize, getMaximumStepsize, getMaxSteps, getMinimumStepsize, getNorm, getScale, getTolerance, setFloor, setInitialStepsize, setMaxSteps, setMinimumStepsize, setNorm, setScale, setTolerance, vnorm

Methods inherited from class java.lang.Object

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

Constructor Details

OdeRungeKutta

public OdeRungeKutta(OdeRungeKutta.Function function)

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

Parameters:

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

Method Details

solve

public void solve(double t,
 double tEnd,
 double[] y)
           throws OdeRungeKutta.ToleranceTooSmallException,
OdeRungeKutta.DidNotConvergeException

Integrates the ODE system from t to tEnd. On all but the first call to solve, the value of t must equal the value of tEnd from the previous call.

Parameters:

t - double specifying the independent variable

tEnd - double specifying the value of t 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.

setMaximumStepsize

public void setMaximumStepsize(double stepsize)

Sets the maximum internal step size.

Overrides:

setMaximumStepsize in class ODE

Parameters:

stepsize - a double specifying the maximum internal step size. stepsize must be greater than zero. Default: stepsize = 2