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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 12, Pages 1955–1973
DOI: https://doi.org/10.31857/S0044466921120073 (Mi zvmmf11324) 		 
This article is cited in 1 scientific paper (total in 1 paper)

General numerical methods

Application of cubic splines on Bakhvalov meshes in the case of a boundary layer

I. A. Blatova, A. I. Zadorinb, E. V. Kitaevac

a Volga State University of Telecommunications and Informatics, 443010, Samara, Russia
b Sobolev Institute of Mathematics (Omsk Branch), Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
c Samara National Research University, 443086, Samara, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466921120073
Abstract: The problem of cubic spline interpolation on Bakhvalov meshes for functions with high gradients is considered. Error estimates are obtained in the class of functions with high gradients in an exponential boundary layer. According to these estimates, the error of a spline can increase indefinitely as a small parameter tends to zero for a fixed number of grid nodes. A modified cubic interpolation spline is proposed, the error of which has an $O(N^{-4})$ estimate uniformly with respect to the small parameter, where $N$ is the number of grid nodes.
Key words: singular perturbation, boundary layer, Bakhvalov mesh, cubic spline, modification, error estimate.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00650
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2019-0009
This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00650) and by the basic research program no. 1.1.3 of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2019-0009).
Received: 12.12.2020
Revised: 12.12.2020
Accepted: 04.08.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 12, Pages 1911–1930
DOI: https://doi.org/10.1134/S096554252112006X
Bibliographic databases:
Document Type: Article
UDC: 519.988
Language: Russian
Citation: I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Application of cubic splines on Bakhvalov meshes in the case of a boundary layer”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 1955–1973; Comput. Math. Math. Phys., 61:12 (2021), 1911–1930
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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