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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2018, Number 3(23), Pages 158–167
DOI: https://doi.org/10.18454/2079-6641-2018-23-3-158-167 (Mi vkam267) 		 
This article is cited in 1 scientific paper (total in 1 paper)

NUMERICAL METHODS OF SOLVING THE PROBLEMS OF MATHEMATICAL PHYSICS

A local one-dimensional scheme for parabolic equation of general form, describing microphysical processes in convective clouds

B. A. Ashabokova, I. D. Taisaevb, M. H. Shhanukov-Lafishevb

a Institute for Informatics and Control of Regional Problems KBNC Russian Academy of Sciences, Nal'chik
b Institute of Applied Mathematics and Automation, Nalchik
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DOI: https://doi.org/10.18454/2079-6641-2018-23-3-158-167
Abstract: This paper considers a locally one-dimensional scheme for a parabolic equation of general form in a p-dimensional parallelepiped.To describe coagulation processes in the cloud, the equation under study involves a non-local source of a specific type [1]. An a priori estimate for the solution to the locally one-dimensional scheme is obtained and its convergence is proved. Sign definiteness for the operator in the principal part of the equation is not assumed.
Keywords: boundary value problem, locally one-dimensional scheme, stability, scheme convergence, approximation error.
Received: 08.06.2018
Bibliographic databases:
Document Type: Article
UDC: 519.63
MSC: 35K10
Language: Russian
Citation: B. A. Ashabokov, I. D. Taisaev, M. H. Shhanukov-Lafishev, “A local one-dimensional scheme for parabolic equation of general form, describing microphysical processes in convective clouds”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 3(23), 158–167
Citation in format AMSBIB
\Bibitem{AshTaiShh18}
\by B.~A.~Ashabokov, I.~D.~Taisaev, M.~H.~Shhanukov-Lafishev
\paper A local one-dimensional scheme for parabolic equation of general form, describing microphysical processes in convective clouds
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2018
\issue 3(23)
\pages 158--167
\mathnet{http://mi.mathnet.ru/vkam267}
\crossref{https://doi.org/10.18454/2079-6641-2018-23-3-158-167}
\elib{https://elibrary.ru/item.asp?id=35604482}
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