This article is cited in 2 papers

General numerical methods

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

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

a</sup> 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

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.

UDC: 519.988

Received: 12.12.2020
Revised: 12.12.2020
Accepted: 04.08.2021

DOI: 10.31857/S0044466921120073

 English version: Computational Mathematics and Mathematical Physics, 2021, 61:12, 1911–1930

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