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Russia Nalchik
Year
2021
Volume
31
Issue
3
Pages
384-408
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Section Mathematics
Title A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation
Author(-s) Beshtokov M.Kh.a
Affiliations Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of the Russian Academy of Sciencesa
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
UDC 35L35
MSC 519.63
DOI 10.35634/vm210303
Received 11 May 2021
Language Russian
Citation Beshtokov M.Kh. A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 3, pp. 384-408.
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