Parabolic spline interpolation for functions with large gradient in the boundary layer
- Authors: Blatov I.A.1, Zadorin A.I.2, Kitaeva E.V.3
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Affiliations:
- Volga State University of Telecommunications and Informatics
- Sobolev Institute of Mathematics, Omsk Branch
- Samara National Research University
- Issue: Vol 58, No 4 (2017)
- Pages: 578-590
- Section: Article
- URL: https://journal-vniispk.ru/0037-4466/article/view/171283
- DOI: https://doi.org/10.1134/S0037446617040036
- ID: 171283
Cite item
Abstract
We consider the problem of Subbotin’s parabolic spline interpolation for functions with large gradient domains. In the case of the common piecewise uniform Shishkin’s mesh we obtain two-sided accuracy estimates for the class of functions with exponential boundary layer. The spline interpolation accuracy estimates are not uniform in a small parameter, while the error itself can grow unboundedly as the small parameter vanishes and the number N of nodes remains fixed. We include the results of some simulations.
About the authors
I. A. Blatov
Volga State University of Telecommunications and Informatics
Author for correspondence.
Email: blatow@mail.ru
Russian Federation, Samara
A. I. Zadorin
Sobolev Institute of Mathematics, Omsk Branch
Email: blatow@mail.ru
Russian Federation, Omsk
E. V. Kitaeva
Samara National Research University
Email: blatow@mail.ru
Russian Federation, Samara
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