This article is cited in 8 papers

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

I. A. Blatov^a, A. I. Zadorin^b, E. V. Kitaeva<sup>c

a</sup> 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.

UDC: 519.652

Received: 30.01.2017

DOI: 10.7868/S0044466918030055

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

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