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Home » Issues » Archive of Issues » 2020 - 2 issue » pp. 158-175

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Russia Nalchik
Year
2020
Volume
30
Issue
2
Pages
158-175
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Section Mathematics
Title Boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator and difference methods for their solution
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 paper is devoted to the construction of approximate solutions of boundary value problems in a rectangle for a loaded modified fractional-order moisture transfer equation with the Bessel operator, which act as mathematical models of the movement of moisture and salts in soils with fractal organization. Difference schemes for differential problems are constructed. The method of energy inequalities is used to derive a priori estimates of solutions to the problems under consideration in differential and difference interpretations. The obtained a priori estimates are followed by uniqueness, stability of the solution from the initial data and the right part, as well as convergence of the solution of the difference problem to the solution of the corresponding differential problem with a speed equal to the order of approximation error. An algorithm for the numerical solution of difference schemes obtained by approximating boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator is constructed.
Keywords boundary value problems, a priori estimation, loaded equations, difference scheme, pseudoparabolic equation, moisture transfer equation, Hallaire's equation, Caputo fractional derivative
UDC 519.63
MSC 35L25
DOI 10.35634/vm200202
Received 11 February 2020
Language Russian
Citation Beshtokov M.Kh. Boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator and difference methods for their solution, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 2, pp. 158-175.
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