Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 39. no. 2. pp. 184–196. ISSN 2079-6641
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: email@example.com, firstname.lastname@example.org, email@example.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.
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.
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© Shhanukov-Lafishev M. H., Lafisheva M. M., Taisaev I. D., 2022
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Shhanukov–Lafishev Mukhamed Habalovich – D. Sci. (Phys. & Math.), Professor, Institute Of Applied Mathematics and Automation of KBSC RAS, Nalchik, Russia, firstname.lastname@example.org, ORCID 0000- 0002-7242-975X.
Lafisheva Madina Mukhammedovna – Ph. D. (Phys. & Math.), Associate Professor of the Department of Applied Mathematics and Informatics, Institute of Artificial Intelligence and Digital Technologies, Kabardino-Balkarian State University named after Kh. M. Berbekov, Nalchik, Russia, email@example.com, ORCID 0000-0002-7230-6629.
Taysaev Idar Djabrailovich – Graduate student of Kabardin–Balkar Scientific Center of Russian Academy of Sciences, Nalchik, Russia, firstname.lastname@example.org, ORCID 0000-0002-0191-8353.