This article is cited in 10 scientific papers (total in 10 papers)
MATHEMATICS
Boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator and difference methods for their solution
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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/vuu717
https://www.mathnet.ru/eng/vuu/v30/i2/p158
This publication is cited in the following 10 articles:
Z. V. Beshtokova, V. A. Vogahova, M. Z. Khudalov, “Difference methods for solving some classes of multidimensional loaded parabolic equations with boundary conditions of the first kind”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2024, no. 2, 25–39
M. Kh. Beshtokov, “Nachalno-kraevye zadachi dlya uravneniya vlagopernosa s drobnymi proizvodnymi raznykh poryadkov i nelokalnym lineinym istochnikom”, Vladikavk. matem. zhurn., 26:3 (2024), 5–23
M. Kh. Beshtokov, “Initial-Boundary Value Problems for the Moisture Transfer Equation with Different Order Fractional Derivatives and Nonlocal Linear Source”, Sib Math J, 65:6 (2024), 1407
M. Kh. Beshtokov, “Chislennye metody resheniya nelokalnykh kraevykh zadach dlya obobschennykh nagruzhennykh uravnenii Allera”, Vladikavk. matem. zhurn., 25:3 (2023), 15–35
Mifodijus Sapagovas, Artūras Štikonas, Olga Štikonienė, “ADI Method for Pseudoparabolic Equation with Nonlocal Boundary Conditions”, Mathematics, 11:6 (2023), 1303
M. Kh. Beshtokov, “Konechno-raznostnyi metod resheniya mnogomernogo psevdoparabolicheskogo uravneniya s granichnymi usloviyami tretego roda”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 502–527
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
M. Kh. Beshtokov, “A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation”, Vestn. Udmurt. Univ.-Mat. Mekh. Kompyuternye Nauk., 31:3 (2021), 384–408
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
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