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Title: On multi-parameter error expansions in finite difference methods for linear Dirichlet problems (English)
Author: Dinh, Ta Van
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 32
Issue: 1
Year: 1987
Pages: 16-24
Summary lang: English
Summary lang: Russian
Summary lang: Czech
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Category: math
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Summary: The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an $n$-dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an ($n$-dimensional) rectangular grid in the directions of the individual axes appear as parameters. (English)
Keyword: error expansion
Keyword: Dirichlet problem
Keyword: selfadjoint
Keyword: central difference scheme
Keyword: finite difference method
MSC: 35J25
MSC: 65N06
MSC: 65N15
idZBL: Zbl 0629.65109
idMR: MR0879326
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Date available: 2008-05-20T18:31:27Z
Last updated: 2015-06-03
Stable URL: http://hdl.handle.net/10338.dmlcz/104232
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Reference: [1] Г. И. Марчук В. В. Шайдуров: Повышение точности решений разностных схем.Москва, Наука, 1979. Zbl 1225.01075
Reference: [2] О. А. Ладыженская H. H. Уралъцева: Линейные и квазилинейные уравнения эллиптического типа.Москва, Наука, 1973. Zbl 1221.53041
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