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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 3, Pages 365–382
DOI: https://doi.org/10.7868/S0044466918030055 (Mi zvmmf10689) 		 
This article is cited in 8 scientific papers (total in 8 papers)

On the parameter-uniform convergence of exponential spline interpolation in the presence of a boundary layer

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

a Povolzhskiy State University of Telecommunications and Informatics, Samara, Russia
b Sobolev Institute of Mathematics, Omsk Branch, Siberian Branch, Russian Academy of Sciences, Omsk, Russia
c Samara State Aerospace University, Samara, Russia
Citations (8)
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DOI: https://doi.org/10.7868/S0044466918030055
Abstract: The paper is concerned with the problem of generalized spline interpolation of functions having large-gradient regions. Splines of the class $C^2$, represented on each interval of the grid by the sum of a second-degree polynomial and a boundary layer function, are considered. The existence and uniqueness of the interpolation $L$-spline are proven, and asymptotically exact two-sided error estimates for the class of functions with an exponential boundary layer are obtained. It is established that the cubic and parabolic interpolation splines are limiting for the solution of the given problem. The results of numerical experiments are presented.
Key words: singular perturbation, boundary layer, exponential spline, error estimate, uniform convergence.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-06584_а
16-01-00727_а
Received: 30.01.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 3, Pages 348–363
DOI: https://doi.org/10.1134/S0965542518030028
Bibliographic databases:
Document Type: Article
UDC: 519.652
Language: Russian
Citation: I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “On the parameter-uniform convergence of exponential spline interpolation in the presence of a boundary layer”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 365–382; Comput. Math. Math. Phys., 58:3 (2018), 348–363
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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