B. A. Ashabokov, A. Kh. Khibiev, M. H. Shhanukov-Lafishev, “A locally one-dimensional scheme for a general parabolic equation describing microphysical processes in convective clouds”, Reports of AIAS, 2021, Volume 21, Issue 4,Pages <nobr>45

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MATH MODELING

A locally one-dimensional scheme for a general parabolic equation describing microphysical processes in convective clouds

B. A. Ashabokov^a, A. Kh. Khibiev^b, M. H. Shhanukov-Lafishev^b

^a Institute of Computer Science and Problems of Regional Management – branch of Federal public budgetary scientific establishment "Federal scientific center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", Nal'chik
^b Institute of Applied Mathematics and Automation, Nalchik

Abstract: A locally one-dimensional difference scheme for a general parabolic equation in a p-dimensional parallelepiped is considered. To describe microphysical processes in convective clouds, non-local (nonlinear) integral sources of a special type are included in the equation under consideration. An a priori estimate for the solution of a locally one-dimensional scheme is obtained and its convergence is proved.

Keywords: boundary value problem, locally one-dimensional scheme, stability, convergence of the scheme, approximation error.

UDC: \udk{УДК 519.63}

DOI: 10.47928/1726-9946-2021-21-4-45-55