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Generalized Spline Interpolation of Functions with Large Gradients in Boundary Layers

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Abstract

The spline interpolation of functions of one variable with large gradients in boundary layers is studied. It is well known that applying polynomial splines to interpolate functions of this kind leads to significant errors when the small parameter is comparable with the grid step size. A generalized spline that is an analogue of a cubic spline is constructed. The spline is exact on the component responsible for large gradients of the function in the boundary layer. The boundary-layer component is considered as a function of a general form; in particular, the case of an exponential boundary layer is treated. The existence, uniqueness, and accuracy of the constructed spline are analyzed.

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Funding

This study was supported by the Fundamental Research Program no. 1.1.3 of the Siberian Branch of the Russian Academy of Sciences, project no. 0314-2019-0009.

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Authors and Affiliations

  1. Volga State University of Telecommunications and Informatics, 443010, Samara, Russia

    I. A. Blatov

  2. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. I. Zadorin

  3. Samara National Research University, 443086, Samara, Russia

    E. V. Kitaeva

Authors
  1. I. A. Blatov
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  2. A. I. Zadorin
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  3. E. V. Kitaeva
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Corresponding authors

Correspondence to I. A. Blatov or A. I. Zadorin.

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Translated by N. Berestova

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Blatov, I.A., Zadorin, A.I. & Kitaeva, E.V. Generalized Spline Interpolation of Functions with Large Gradients in Boundary Layers. Comput. Math. and Math. Phys. 60, 411–426 (2020). https://doi.org/10.1134/S0965542520030057

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  • DOI: https://doi.org/10.1134/S0965542520030057

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