MathTL::WMethodStageEquationHelper< VECTOR > Class Template Reference

#include <w_method.h>

Inheritance diagram for MathTL::WMethodStageEquationHelper< VECTOR >:

List of all members.

Public Member Functions
virtual	~WMethodStageEquationHelper ()=0
	purely virtual destructor
virtual void	solve_W_stage_equation (const AbstractIVP< VECTOR > *ivp, const double t, const VECTOR &v, const double alpha, const VECTOR &y, const double tolerance, VECTOR &x) const =0
virtual void	approximate_ft (const AbstractIVP< VECTOR > *ivp, const double t, const VECTOR &v, const double tolerance, VECTOR &result) const =0

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Detailed Description

template<class VECTOR>
class MathTL::WMethodStageEquationHelper< VECTOR >

Abstract helper class for (adaptive) solvers of the W-(or ROW-) method stage equations

(alpha*I-T)x=y.

In a W-method, one replaces the exact Jacobian J=f_v(t,v) by an maybe crude approximation T. The derivative f_t(t,v) will also be approximated by a vector g (often even by zero).

In practice, it is possible (but not necessary) to make the concrete instance of AbstractIVP under consideration also a descendant from this helper class. For example, the class ROWMethod uses a special WMethodStageEquationHelper class, see row_method.h for details.

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Member Function Documentation

template<class VECTOR>

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

Approximation of the temporal derivative f_t(t,v) (up to some tolerance w.r.t. ||.||_2, often denoted as g). In practice, g will often be chosen as zero, for stability reasons (reducing the overall consistency order of the W-method).

Implemented in MathTL::ROWMethod< VECTOR >.

template<class VECTOR>

virtual void MathTL::WMethodStageEquationHelper< VECTOR >::solve_W_stage_equation	(	const AbstractIVP< VECTOR > *	ivp,
		const double	t,
		const VECTOR &	v,
		const double	alpha,
		const VECTOR &	y,
		const double	tolerance,
		VECTOR &	x
	)		const [pure virtual]

(adaptive) solver for one of the systems (alpha*I-T)x=y, implicitly this also specifies the approximation T to the Jacobian f_v(t,v)

Implemented in MathTL::ROWMethod< VECTOR >.

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

• numerics/w_method.h
• numerics/w_method.cpp