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This article is cited in 4 scientific papers (total in 4 papers)
MATHEMATICS
Numerical-analytical method for solving boundary value problem for the generalized moisture transport equation
M. A. Kerefova, S.Kh. Gekkievab a Department of Applied Mathematics and Informatics,
Kabardino-Balkarian State University named after H. M. Berbekov, ul. Chernyshevskogo, 173, Nalchik, 360004, Russia
b Institute of Applied Mathematics
and Automation of Kabardin-Balkar Scientific Center of RAS, ul. Shortanova, 89 a, Nalchik, 360000,
Russia
Abstract:
The paper studies qualitatively new equations of moisture transfer, which generalize the Aller and Aller-Lykov equations. The generalization contributes to revealing in the original equations the specific features of the studied massifs, their structure, physical properties, processes occurring in them through the introduction of the notion of the rates of change of the fractal dimension. We have obtained solutions to the constant coefficient difference equations as a system arising when using the method of lines for the equations with a Riemann-Liouville time fractional derivative with boundary conditions of the first kind. A priori estimates are obtained that imply convergence of the obtained solutions to systems of ordinary differential equations with variable fractional coefficients. Numerical tests have been carried out to confirm theoretical results of the study.
Keywords:
generalized Aller moisture transfer equation, Aller-Lykov equation, fractional order derivative, method of lines, a priori estimate.
Received: 23.12.2020
Citation:
M. A. Kerefov, S.Kh. Gekkieva, “Numerical-analytical method for solving boundary value problem for the generalized moisture transport equation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:1 (2021), 19–34
Linking options:
https://www.mathnet.ru/eng/vuu752 https://www.mathnet.ru/eng/vuu/v31/i1/p19
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Abstract page: | 330 | Full-text PDF : | 173 | References: | 39 |
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