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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 4, Pages 671–692 (Mi zvmmf306)  
This article is cited in 1 scientific paper (total in 1 paper)

On the stability of the $\sigma$-scheme with transparent boundary conditions for parabolic equations

A. A. Zlotnik

Department of Applied Mathematics, Russian State Social University, ul. V. Pika. 4, Moscow, 129226, Russia
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Abstract: Initial-boundary value problems for self-adjoint parabolic equations on a semiaxis and a semibounded strip are considered. For finite-difference $\sigma$-schemes, an alternative method for stating approximate transparent boundary conditions is suggested and conditions ensuring unconditional stability in the energy norm with respect to the initial data and free terms for a weight $\sigma\ge1/2$ are presented. The validity of these stability conditions in the case of discrete transparent boundary conditions is proved (by several methods), and the derivation of the latter conditions is revisited.
Key words: stability, finite-difference $\sigma$-scheme, approximate and discrete transparent boundary conditions, parabolic equations, unbounded domains.
Received: 20.04.2006
Revised: 08.11.2006
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 4, Pages 644–663
DOI: https://doi.org/10.1134/S0965542507040100
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: A. A. Zlotnik, “On the stability of the $\sigma$-scheme with transparent boundary conditions for parabolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007), 671–692; Comput. Math. Math. Phys., 47:4 (2007), 644–663
Citation in format AMSBIB
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\by A.~A.~Zlotnik
\paper On the stability of the $\sigma$-scheme with transparent boundary conditions for parabolic equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 4
\pages 671--692
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2376631}
\zmath{https://zbmath.org/?q=an:05200951}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 4
\pages 644--663
\crossref{https://doi.org/10.1134/S0965542507040100}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248150851}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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