MathTL::SturmBVP Class Reference

#include <sturm_bvp.h>

Inheritance diagram for MathTL::SturmBVP:

List of all members.

Public Member Functions
virtual	~SturmBVP ()
virtual double	p (const double t) const =0
virtual double	p_prime (const double t) const =0
virtual double	q (const double t) const =0
virtual double	g (const double t) const =0
virtual double	alpha0 () const =0
virtual double	alpha1 () const =0
virtual double	beta0 () const =0
virtual double	beta1 () const =0
void	apply_f (const double t, const Point< 2 > &v, Point< 2 > &result) const
	right-hand side as a general BVP (inherited)
void	apply_A (const Point< 2 > &v, Point< 2 > &result) const
	left boundary condition matrix (inherited)
void	apply_B (const Point< 2 > &v, Point< 2 > &result) const
	right boundary condition matrix (inherited)

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Detailed Description

Abstract base class for a (real valued) Sturm boundary value problem on [0,1]

-(py')'(t) + q(t)y(t) = g(t), 0 <= t <= 1

with third order homogeneous boundary conditions

R_0y := alpha_0*y(0) + alpha_1*p(0)*y'(0) = 0 R_1y := beta_0 *y(1) + beta_1 *p(1)*y'(1) = 0

You have to take care that for a fundamental system {y_1,y_2} of the diff. eq., one has a nontrivial determinant R_0y_1*R_1y_2-R_1y_1*R_0y_2 != 0.

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Constructor & Destructor Documentation

MathTL::SturmBVP::~SturmBVP

(

)

[inline, virtual]

virtual destructor

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Member Function Documentation

virtual double MathTL::SturmBVP::alpha0

(

)

const [pure virtual]

left boundary condition coefficient 0

Implemented in MathTL::SimpleSturmBVP, and TestProblem.

virtual double MathTL::SturmBVP::alpha1

(

)

const [pure virtual]

left boundary condition coefficient 1

Implemented in MathTL::SimpleSturmBVP, and TestProblem.

virtual double MathTL::SturmBVP::beta0

(

)

const [pure virtual]

right boundary condition coefficient 0

Implemented in MathTL::SimpleSturmBVP, and TestProblem.

virtual double MathTL::SturmBVP::beta1

(

)

const [pure virtual]

left boundary condition coefficient 1

Implemented in MathTL::SimpleSturmBVP, and TestProblem.

virtual double MathTL::SturmBVP::g

(

const double

t

)

const [pure virtual]

right-hand side

Implemented in MathTL::SimpleSturmBVP, TestProblem2, and TestProblem.

virtual double MathTL::SturmBVP::p

(

const double

t

)

const [pure virtual]

diffusion coefficient

Implemented in MathTL::SimpleSturmBVP, TestProblem2, and TestProblem.

virtual double MathTL::SturmBVP::p_prime

(

const double

t

)

const [pure virtual]

first derivative of the diffusion coefficient

Implemented in MathTL::SimpleSturmBVP, TestProblem2, and TestProblem.

virtual double MathTL::SturmBVP::q

(

const double

t

)

const [pure virtual]

reaction coefficient

Implemented in MathTL::SimpleSturmBVP, TestProblem2, and TestProblem.

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

• numerics/sturm_bvp.h
• numerics/sturm_bvp.cpp