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Russia Nalchik
Year
2021
Volume
31
Issue
1
Pages
19-34
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Section Mathematics
Title Numerical-analytical method for solving boundary value problem for the generalized moisture transport equation
Author(-s) Kerefov M.A.a, Gekkieva S.K.b
Affiliations Kabardino-Balkarian State Universitya, Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of the Russian Academy of Sciencesb
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
UDC 517.95
MSC 35C99
DOI 10.35634/vm210102
Received 23 December 2020
Language Russian
Citation Kerefov M.A., Gekkieva S.K. Numerical-analytical method for solving boundary value problem for the generalized moisture transport equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 1, pp. 19-34.
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