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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
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.
Received: 11.05.2021
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
Linking options:
https://www.mathnet.ru/eng/vuu776 https://www.mathnet.ru/eng/vuu/v31/i3/p384
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