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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/vuu776
https://www.mathnet.ru/eng/vuu/v31/i3/p384
This publication is cited in the following 2 articles:
Mifodijus Sapagovas, Artūras Štikonas, Olga Štikonienė, “ADI Method for Pseudoparabolic Equation with Nonlocal Boundary Conditions”, Mathematics, 11:6 (2023), 1303
M. Kh. Beshtokov, “Konechno-raznostnyi metod resheniya mnogomernogo psevdoparabolicheskogo uravneniya s granichnymi usloviyami tretego roda”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 502–527
Citation in format AMSBIB
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