OdeAdamsGear Class

OdeAdamsGear Class

Extension of the ODE class to solve a stiff initial-value problem for ordinary differential equations using the Adams-Gear methods.

Inheritance Hierarchy

SystemObject
Imsl.MathODE
Imsl.MathOdeAdamsGear

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

Syntax

C++

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[SerializableAttribute]
public class OdeAdamsGear : ODE

<SerializableAttribute>
Public Class OdeAdamsGear
	Inherits ODE

[SerializableAttribute]
public ref class OdeAdamsGear : public ODE

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

The OdeAdamsGear type exposes the following members.

Constructors

	Name	Description
	OdeAdamsGear	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 ODESetMaximumStepsize(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.)
	IntegrationMethod	The integration method.
	MaximumFunctionEvaluations	The maximum number of function evaluations of allowed.
	MaxOrder	The highest order formula to use of implicit Adams type or BDF type.
	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.)
	NumberOfFcnEvals	Returns the number of function evaluations of made.
	NumberOfJacobianEvals	Returns the number of Jacobian matrix evaluations used.
	NumberOfSteps	Returns the number of internal steps taken.
	Scale	The scaling factor. (Inherited from ODE.)
	SolveMethod	The method for solving the formula equations.
	Tolerance	The error tolerance. (Inherited from ODE.)

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Remarks

Class OdeAdamsGear 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 conditions for

at the starting value for

. The class attempts to keep the global error proportional to a user-specified tolerance. The proportionality depends on the differential equation and the range of integration.

The code is based on using backward difference formulas not exceeding order five as outlined in Gear (1971) and implemented by Hindmarsh (1974). There is an optional use of the code that employs implicit Adams formulas. This use is intended for nonstiff problems with expensive functions .

Reference

Imsl.Math Namespace

Other Resources

Example