MathTL::AbstractIVP< VECTOR > Class Template Reference

#include <ivp.h>

List of all members.

Public Member Functions
virtual	~AbstractIVP ()=0
virtual void	evaluate_f (const double t, const VECTOR &v, const double tolerance, VECTOR &result) const =0
virtual void	evaluate_ft (const double t, const VECTOR &v, const double tolerance, VECTOR &result) const =0
virtual void	solve_ROW_stage_equation (const double t, const VECTOR &v, const double alpha, const VECTOR &y, const double tolerancs, VECTOR &result) const =0
Public Attributes
VECTOR	u0

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Detailed Description

template<class VECTOR>
class MathTL::AbstractIVP< VECTOR >

Abstract base class for general initial value problems

u'(t) = f(t, u(t)), 0 < t <= T u(0) = u_0

where u:[0,T]->V.

The signature of AbstractIVP is designed to be used in (derivations of) the class OneStepScheme, especially for Runge-Kutta and linearly implicit methods.

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Constructor & Destructor Documentation

template<class VECTOR >

MathTL::AbstractIVP< VECTOR >::~AbstractIVP

(

)

[pure virtual]

virtual destructor

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Member Function Documentation

template<class VECTOR>

virtual void MathTL::AbstractIVP< VECTOR >::evaluate_f	(	const double	t,
		const VECTOR &	v,
		const double	tolerance,
		VECTOR &	result
	)		const [pure virtual]

evaluate the right--hand side f at (t,v), up to some tolerance (w.r.t. the ||.||_2 norm)

Implemented in Arenstorf, Circle, Expo, SquareRoot2, SquareRoot, and Dahlquist.

template<class VECTOR>

virtual void MathTL::AbstractIVP< VECTOR >::evaluate_ft	(	const double	t,
		const VECTOR &	v,
		const double	tolerance,
		VECTOR &	result
	)		const [pure virtual]

evaluate the derivative f_t at (t,v), up to some tolerance (w.r.t. the ||.||_2 norm)

Implemented in Arenstorf, Circle, Expo, SquareRoot2, SquareRoot, and Dahlquist.

template<class VECTOR>

virtual void MathTL::AbstractIVP< VECTOR >::solve_ROW_stage_equation	(	const double	t,
		const VECTOR &	v,
		const double	alpha,
		const VECTOR &	y,
		const double	tolerancs,
		VECTOR &	result
	)		const [pure virtual]

Up to a given tolerance (w.r.t. the ||.||_2 norm), solve the special linear system

(alpha*I-J)x = y,

where J = f(t,v) is the (exact) Jacobian of f. This routine will primarily be used to solve the stage equations of an ROW-method.

Implemented in Arenstorf, Circle, Expo, SquareRoot2, SquareRoot, and Dahlquist.

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Member Data Documentation

template<class VECTOR>

VECTOR MathTL::AbstractIVP< VECTOR >::u0

initial value

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The documentation for this class was generated from the following files:

• numerics/ivp.h
• numerics/ivp.cpp