Email this article Numerical method for solving an initial-boundary value problem for a multidimensional loaded parabolic equation of a general form with conditions of the third kind
- Authors: Beshtokova Z.V.1,2
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Affiliations:
- North-Caucasus Center for Mathematical Research, North-Caucasus Federal University
- Kabardino-Balkarian State University named after H.M. Berbekov
- Issue: Vol 26, No 1 (2022)
- Pages: 7-36
- Section: Differential Equations and Mathematical Physics
- URL: https://journal-vniispk.ru/1991-8615/article/view/103401
- DOI: https://doi.org/10.14498/vsgtu1908
- ID: 103401
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Abstract
An initial-boundary value problem is studied for a multidimensional loaded parabolic equation of general form with boundary conditions of the third kind. For a numerical solution, a locally one-dimensional difference scheme by A.A. Samarskii with order of approximation is constructed. Using the method of energy inequalities, we obtain a priori estimates in the differential and difference interpretations, which imply uniqueness, stability, and convergence of the solution of the locally one-dimensional difference scheme to the solution of the original differential problem in the norm at a rate equal to the order of approximation of the difference scheme. An algorithm for the computational solution is constructed and numerical calculations of test cases are carried out, illustrating the theoretical calculations obtained in this work.
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##article.viewOnOriginalSite##About the authors
Zaryana V. Beshtokova
North-Caucasus Center for Mathematical Research, North-Caucasus Federal University; Kabardino-Balkarian State University named after H.M. Berbekov
Author for correspondence.
Email: zarabaeva@yandex.ru
ORCID iD: 0000-0001-8020-4406
SPIN-code: 4704-0910
Scopus Author ID: 57195928671
ResearcherId: AAH-9338-2020
Researcher Dept. of Computational Methods; Postgraduate Student
Russian Federation, 1, Pushkin str., Stavropol, 355017; 173, Chernyshevsky str., Nalchik, 360004References
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