Beshtokov M.Kh., Vodakhova V.A., Shkhanukov-Lafishev M.Kh. Summary Approximation Method for a Third Order Multidimensional Pseudoparabolic Equation

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https://doi.org/10.15688/mpcm.jvolsu.2021.4.1

Murat Kh. Beshtokov
Candidate of Physical and Mathematical Sciences, Associate Professor, Leading
Researcher,
Department of Computational Methods,
Institute of Applied Mathematics and Automation,
Kabardino-Balkarian Scientific Center of RAS
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https://orcid.org/0000-0003-2968-9211 
Shortanova St, 89a, 360000 Nalchik, Russian Federation

Valentina A. Vodakhova
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Algebra and Differential Equations,
Institute of Physics and Mathematics,
Kabardino-Balkarian State University
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Chernyshevskogo St, 175, 360000 Nalchik, Russian Federation

Mukhamed Kh. Shkhanukov-Lafishev
Doctor of Physical and Mathematical Sciences, Professor,
Chief Researcher, Department of Mathematical Modeling of Geophysical Processes,
Institute of Applied Mathematics and Automation,
Kabardino-Balkarian Scientific Center of RAS
This email address is being protected from spambots. You need JavaScript enabled to view it.  
Shortanova St, 89a, 360000 Nalchik, Russian Federation

Abstract. In this paper we study the first initial-boundary value problem for a multidimensional pseudoparabolic equation of the third order. Assuming the existence of a regular solution to the problem posed, an a priori estimate is obtained in differential form, which implies the uniqueness and stability of the solution with respect to the right-hand side and initial data. A locally onedimensional difference scheme is constructed and an a priori estimate in the difference form is obtained for its solution. The stability and convergence of the locally one-dimensional difference scheme are proved. Numerical calculations are performed using test examples to illustrate the theoretical calculations obtained in this work.

Key words: boundary value problems, a priori estimation, modified moisture transfer equation, pseudoparabolic equation, locally one-dimensional scheme, stability and convergence of the scheme, schema additivity.

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Summary Approximation Method for a Third Order Multidimensional Pseudoparabolic Equation by Beshtokov M.Kh., Vodakhova V.A., Shkhanukov-Lafishev M.Kh. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 24 No. 4 2021, pp. 5-18

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