Cubic spline interpolation of functions with high gradients in boundary layers
- 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), Siberian Branch
- Samara State University
- Issue: Vol 57, No 1 (2017)
- Pages: 7-25
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/178852
- DOI: https://doi.org/10.1134/S0965542517010043
- ID: 178852
Cite item
Abstract
The cubic spline interpolation of grid functions with high-gradient regions is considered. Uniform meshes are proved to be inefficient for this purpose. In the case of widely applied piecewise uniform Shishkin meshes, asymptotically sharp two-sided error estimates are obtained in the class of functions with an exponential boundary layer. It is proved that the error estimates of traditional spline interpolation are not uniform with respect to a small parameter, and the error can increase indefinitely as the small parameter tends to zero, while the number of nodes N is fixed. A modified cubic interpolation spline is proposed, for which O((ln N/N)4) error estimates that are uniform with respect to the small parameter are obtained.
About the authors
I. A. Blatov
Volga State University of Telecommunications and Informatics
Author for correspondence.
Email: blatow@mail.ru
Russian Federation, Samara, 443090
A. I. Zadorin
Sobolev Institute of Mathematics (Omsk Branch), Siberian Branch
Author for correspondence.
Email: zadorin@ofim.oscsbras.ru
Russian Federation, Omsk, 644043
E. V. Kitaeva
Samara State University
Email: zadorin@ofim.oscsbras.ru
Russian Federation, Samara, 443086
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