OdeRungeKutta Class

OdeRungeKutta Class

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

Inheritance Hierarchy

System.Object
Imsl.Math.ODE
Imsl.Math.OdeRungeKutta

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class OdeRungeKutta : ODE

<SerializableAttribute>
Public Class OdeRungeKutta
	Inherits ODE

[SerializableAttribute]
public ref class OdeRungeKutta : public ODE

[<SerializableAttribute>]
type OdeRungeKutta =  
    class
        inherit ODE
    end

The OdeRungeKutta type exposes the following members.

Constructors

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

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	ExamineStep	Called before and after each internal step. (Inherited from ODE.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetMaximumStepsize	Returns the maximum internal step size. (Inherited from ODE.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	SetMaximumStepsize	Sets the maximum internal step size. (Overrides ODE.SetMaximumStepsize(Double).)
	Solve	Integrates the ODE system from t to tEnd.
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	Vnorm	Returns the norm of a vector. (Inherited from ODE.)

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Properties

	Name	Description
	Floor	The value used in the norm computation. (Inherited from ODE.)
	InitialStepsize	The initial internal step size. (Inherited from ODE.)
	MaxSteps	The maximum number of internal steps allowed. (Inherited from ODE.)
	MinimumStepsize	The minimum internal step size. (Inherited from ODE.)
	NormMethod	The error norm. (Inherited from ODE.)
	Scale	The scaling factor. (Inherited from ODE.)
	Tolerance	The error tolerance. (Inherited from ODE.)

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Remarks

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.

Reference

Imsl.Math Namespace

Other Resources

Example