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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Pages 1566–1575 (Mi zvmmf11134)  

Total approximation method for an equation describing droplet breakup and freezing in convective clouds

B. A. Ashabokova, A. Kh. Khibievb, M. H. Shhanukov-Lafishevb

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 scheme for a general parabolic equation in a $p$ -dimensional parallelepiped is considered. A special nonlocal integral source is added to the considered equation to describe droplet breakup and freezing in convective clouds. An a priori estimate for the solution of the locally one-dimensional scheme is obtained, and its convergence is proved.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 19-31-90094
This work was supported by the Russian Foundation for Basic Research, project no. 19-31-90094.


DOI: https://doi.org/10.31857/S0044466920090057


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1518–1527

Bibliographic databases:

UDC: 519.63
Received: 11.12.2019
Revised: 03.02.2020
Accepted:09.04.2020

Citation: B. A. Ashabokov, A. Kh. Khibiev, M. H. Shhanukov-Lafishev, “Total approximation method for an equation describing droplet breakup and freezing in convective clouds”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1566–1575; Comput. Math. Math. Phys., 60:9 (2020), 1518–1527

Citation in format AMSBIB
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\paper Total approximation method for an equation describing droplet breakup and freezing in convective clouds
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 9
\pages 1566--1575
\mathnet{http://mi.mathnet.ru/zvmmf11134}
\crossref{https://doi.org/10.31857/S0044466920090057}
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