Finite difference, finite element and finite volume methods applied to two-point boundary value problems

This paper considers the finite difference, finite element and finite volume methods applied to the two-point boundary value problem − d dx p(x) du dx =f(x), a<x<b, u(a)=u(b)=0. By using an inversion formula of a nonsingular tridiagonal matrix, explicit expressions of approximate solutions by...

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Vydané v:	Journal of computational and applied mathematics Ročník 139; číslo 1; s. 9 - 19
Hlavní autori:	Fang, Qing, Tsuchiya, Takuya, Yamamoto, Tetsuro
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.02.2002 Elsevier
Predmet:	Exact sciences and technology Finite difference methods Finite element methods Finite volume methods Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Sciences and techniques of general use Finite element methods 65N30 Finite volume methods 65N06 Finite difference methods Finite element method Finite volume method Boundary value problem Error estimation Two point boundary value problem Finite difference method
ISSN:	0377-0427, 1879-1778
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Popis
Shrnutí:	This paper considers the finite difference, finite element and finite volume methods applied to the two-point boundary value problem − d dx p(x) du dx =f(x), a<x<b, u(a)=u(b)=0. By using an inversion formula of a nonsingular tridiagonal matrix, explicit expressions of approximate solutions by three methods are given, which lead to a unified understanding of these methods as well as their unified error estimates. Numerical examples are also given.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0377-0427 1879-1778
DOI:	10.1016/S0377-0427(01)00392-2