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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2020, Volume 30, Issue 2, Pages 158–175 (Mi vuu717)  

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator and difference methods for their solution

M. Kh. Beshtokov

Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, ul. Shortanova, 89 A, Nalchik, 360000, Russia

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.

DOI: https://doi.org/10.35634/vm200202

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Bibliographic databases:

UDC: 519.63
MSC: 35L25
Received: 11.02.2020

Citation: M. Kh. Beshtokov, “Boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator and difference methods for their solution”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:2 (2020), 158–175

Citation in format AMSBIB
\Bibitem{Bes20}
\by M.~Kh.~Beshtokov
\paper Boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator and difference methods for their solution
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 2
\pages 158--175
\mathnet{http://mi.mathnet.ru/vuu717}
\crossref{https://doi.org/10.35634/vm200202}


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    This publication is cited in the following articles:
    1. S. Kh. Gekkieva, M. M. Karmokov, M. A. Kerefov, “Ob odnoi kraevoi zadache dlya obobschennogo uravneniya Allera”, Vestn. SamU. Estestvennonauchn. ser., 26:2 (2020), 7–14  mathnet  crossref  elib
    2. M. A. Kerefov, S. Kh. Gekkieva, “Chislenno-analiticheskii metod resheniya kraevoi zadachi dlya obobschennykh uravnenii vlagoperenosa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:1 (2021), 19–34  mathnet  crossref
    3. M. Kh. Beshtokov, “Chislennyi metod resheniya vtoroi nachalno-kraevoi zadachi dlya mnogomernogo psevdoparabolicheskogo uravneniya tretego poryadka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:3 (2021), 384–408  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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