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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 3, Pages 413–428 (Mi zvmmf11045)  

Generalized spline interpolation of functions with large gradients in boundary layers

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

a Volga State University of Telecommunications and Informatics, Samara, 443010 Russia
b Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
c Samara National Research University, Samara, 443086 Russia

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.

Key words: function of one variable, boundary layer, small parameter, generalized spline, error estimate.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 0314-2019-0009
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.


DOI: https://doi.org/10.31857/S0044466920030059


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:3, 411–426

Bibliographic databases:

UDC: 519.652
Received: 14.03.2019
Revised: 02.09.2019
Accepted:18.11.2019

Citation: I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Generalized spline interpolation of functions with large gradients in boundary layers”, Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020), 413–428; Comput. Math. Math. Phys., 60:3 (2020), 411–426

Citation in format AMSBIB
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\pages 413--428
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