Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 39. no. 2. pp. 184–196. ISSN 2079-6641

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MSC 76M20

Research Article

Locally one-dimensional schemes for an equation describing coagulation processes in convective clouds with “memory”

M. H. Shhanukov-Lafishev¹, M. M. Lafisheva², I. D. Taisaev³

¹Institute of Applied Mathematics and Automation of KBSC RAS, 360000, Kabardino-Balkar Republic, Nalchik, Shortanova str., 89-A, Russia
²Kabardino-Balkar State University, 360004, Kabardino-Balkar Republic, Nalchik, Cherhyshevskaya str., 179, Russia
³Kabardin-Balkar Scientific Center of KBSC RAS, 360002, Kabardino-Balkar Republic, Nalchik, Balkarova str., 2, Russia

E-mail: taisauti@yandex.ru, lafishevamadina@gmail.com, idar0792@gmail.com

The paper considers a locally one-dimensional difference scheme for a general parabolic equation in a p-dimensional parallelepiped. To describe coagulation processes in media with “memory”, non-local sources of a special type are included in the equation. An a priori estimate is obtained for solving the corresponding difference scheme, which implies its convergence.

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

DOI: 10.26117/2079-6641-2022-39-2-184–196

Original article submitted: 29.04.2022

Revision submitted: 28.08.2022

For citation. Shhanukov–Lafishev M. H., Lafisheva M. M., Taisaev I. D. Locally onedimensional schemes for an equation describing coagulation processes in convective clouds with “memory”. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 184–196. DOI: 10.26117/2079-6641-2022-39-2-184–196

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Shhanukov-Lafishev M. H., Lafisheva M. M., Taisaev I. D., 2022

References

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