Summary Approximation Method for a Third Order Multidimensional Pseudoparabolic Equation

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...

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Bibliographic Details
Published in:Mathematical Physics and Computer Modeling Vol. 24; no. 4; pp. 5 - 18
Main Authors: Beshtokov, Murat, Vodakhova, Valentina, Shkhanukov-Lafishev, Mukhamed
Format: Journal Article
Language:English
Published: Volgograd Volgograd State University 01.12.2021
Subjects:
Approximation
Boundary value problems
Mathematical analysis
Stability
ISSN:2587-6325, 2587-6902
Online Access:Get full text
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Summary: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.
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ISSN:2587-6325
2587-6902
DOI:10.15688/mpcm.jvolsu.2021.4.1