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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 4, Pages 502–527
DOI: https://doi.org/10.35634/vm220402 (Mi vuu823) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Finite-difference method for solving a multidimensional pseudoparabolic equation with boundary conditions of the third kind

M. Kh. Beshtokov

North-Caucasus Federal University, North-Caucasus Center for Mathematical Research, ul. Pushkina, 1, Stavropol, 355017, Russia
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DOI: https://doi.org/10.35634/vm220402
Abstract: We study an initial-boundary value problem for a multidimensional pseudoparabolic equation with variable coefficients and boundary conditions of the third kind. The multidimensional pseudoparabolic equation is reduced to an integro-differential equation with a small parameter. It is shown that as the small parameter tends to zero, the solution of the resulting modified problem converges to the solution of the original problem. For an approximate solution of the obtained problem, a locally one-dimensional difference scheme by A. A. Samarsky is constructed. An a priori estimate is obtained by the method of energy inequalities, from which the uniqueness, stability, and convergence of the solution of the locally one-dimensional difference scheme to the solution of the original differential problem follow. For a two-dimensional problem, an algorithm for the numerical solution of the initial-boundary value problem for a pseudoparabolic equation with conditions of the third kind is developed.
Keywords: pseudoparabrolic equation, Hallaire's equation, locally one-dimensional scheme, stability, convergence of difference scheme, sum approximation method.
Received: 26.07.2022
Accepted: 05.10.2022
Bibliographic databases:
Document Type: Article
UDC: 519.63
MSC: 35L35
Language: Russian
Citation: M. Kh. Beshtokov, “Finite-difference method for solving a multidimensional pseudoparabolic equation with boundary conditions of the third kind”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:4 (2022), 502–527
Citation in format AMSBIB
\Bibitem{Bes22}
\by M.~Kh.~Beshtokov
\paper Finite-difference method for solving a multidimensional pseudoparabolic equation with boundary conditions of the third kind
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2022
\vol 32
\issue 4
\pages 502--527
\mathnet{http://mi.mathnet.ru/vuu823}
\crossref{https://doi.org/10.35634/vm220402}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4534868}
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  • https://www.mathnet.ru/eng/vuu/v32/i4/p502
    • This publication is cited in the following articles:
    1. Mifodijus Sapagovas, Artūras Štikonas, Olga Štikonienė, “ADI Method for Pseudoparabolic Equation with Nonlocal Boundary Conditions”, Mathematics, 11:6 (2023), 1303  crossref
    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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