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Home » Issues » Archive of Issues » 2022 - 4 issue » pp. 502-527

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Russia Stavropol
Year
2022
Volume
32
Issue
4
Pages
502-527
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Section Mathematics
Title Finite-difference method for solving a multidimensional pseudoparabolic equation with boundary conditions of the third kind
Author(-s) Beshtokov M.Kh.a
Affiliations North-Caucasus Federal Universitya
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
UDC 519.63
MSC 35L35
DOI 10.35634/vm220402
Received 26 July 2022
Language Russian
Citation Beshtokov M.Kh. Finite-difference method for solving a multidimensional pseudoparabolic equation with boundary conditions of the third kind, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 4, pp. 502-527.
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