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JOURNALS // Vestnik KRAUNC. Fiziko-Matematicheskie Nauki // Archive

Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018 Number 3(23), Pages 158–167 (Mi vkam267)

This article is cited 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

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.

UDC: 519.63

MSC: 35K10

Received: 08.06.2018

DOI: 10.18454/2079-6641-2018-23-3-158-167



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