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.
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
\Bibitem{KerGek21}
\by M.~A.~Kerefov, S.Kh.~Gekkieva
\paper Numerical-analytical method for solving boundary value problem for the generalized moisture transport equation
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 1
\pages 19--34
\mathnet{http://mi.mathnet.ru/vuu752}
\crossref{https://doi.org/10.35634/vm210102}
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https://www.mathnet.ru/eng/vuu752
https://www.mathnet.ru/eng/vuu/v31/i1/p19
This publication is cited in the following 4 articles:
A. M. Romanenkov, “Gradient in the Problem of Controlling Processes Described by Linear
Pseudohyperbolic Equations”, Diff Equat, 60:2 (2024), 215
A. M. Romanenkov, “Gradient in the problem of controlling processes described by linear pseudohyperbolic equations”, Differencialʹnye uravneniâ, 60:2 (2024), 224
M. A. Kerefov, S. Kh. Gekkieva, B. M. Kerefov, “Pervaya kraevaya zadacha dlya uravneniya Allera—Lykova s drobnoi proizvodnoi Kaputo”, Materialy Mezhdunarodnoi konferentsii «Klassicheskaya i sovremennaya geometriya», posvyaschennoi 100-letiyu so dnya rozhdeniya professora Levona Sergeevicha Atanasyana (15 iyulya 1921 g.—5 iyulya 1998 g.). Moskva, 1–4 noyabrya 2021 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 221, VINITI RAN, M., 2023, 63–70
S.Kh. Gekkieva, M. A. Kerefov, F. M. Nakhusheva, “Local and nonlocal boundary value problems for generalized Aller–Lykov equation”, Ufa Math. J., 15:1 (2023), 21–33
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