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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, Volume 31, Issue 3, Pages 384–408
DOI: https://doi.org/10.35634/vm210303
(Mi vuu776)
 

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation

M. Kh. Beshtokov

Institute of Applied Mathematics and Automation, Kabardino-Balkaria Scientific Center of the Russian Academy of Sciences, ul. Shortanova, 89 A, Nalchik, 360000, Russia
Full-text PDF (356 kB) Citations (2)
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Abstract: The work is devoted to the study of the second initial-boundary value problem for a general-form third-order differential equation of pseudoparabolic type with variable coefficients in a multidimensional domain with an arbitrary boundary. In this paper, a multidimensional pseudoparabolic equation is reduced to an integro-differential equation with a small parameter, and a locally one-dimensional difference scheme by A. A. Samarskii is used. Using the maximum principle, an a priori estimate is obtained for the solution of a locally one-dimensional difference scheme in the uniform metric in the $C$ norm. The stability and convergence of the locally one-dimensional difference scheme are proved.
Keywords: pseudoparabolic equation, moisture transfer equation, locally one-dimensional scheme, stability, convergence of the difference scheme, additivity of the scheme.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-53007
The reported study was funded by RFBR and NSFC, project no. 20-51-53007.
Received: 11.05.2021
Document Type: Article
UDC: 519.63
MSC: 35L35
Language: Russian
Citation: M. Kh. Beshtokov, “A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:3 (2021), 384–408
Citation in format AMSBIB
\Bibitem{Bes21}
\by M.~Kh.~Beshtokov
\paper A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 3
\pages 384--408
\mathnet{http://mi.mathnet.ru/vuu776}
\crossref{https://doi.org/10.35634/vm210303}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    Full-text PDF :129
    References:32
     
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