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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 3, Pages 365–382 (Mi zvmmf10689)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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


DOI: https://doi.org/10.7868/S0044466918030055

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:3, 348–363

Bibliographic databases:

UDC: 519.652
Received: 30.01.2017

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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\pages 365--382
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Blatov I.A., Zadorin A.I., Kitaeva E.V., Mechanical Science and Technology Update (Mstu-2018), Journal of Physics Conference Series, 1050, IOP Publishing Ltd, 2018  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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