Cubic spline interpolation of functions with high gradients in boundary layers
- 作者: Blatov I.A.1, Zadorin A.I.2, Kitaeva E.V.3
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隶属关系:
- Volga State University of Telecommunications and Informatics
- Sobolev Institute of Mathematics (Omsk Branch), Siberian Branch
- Samara State University
- 期: 卷 57, 编号 1 (2017)
- 页面: 7-25
- 栏目: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/178852
- DOI: https://doi.org/10.1134/S0965542517010043
- ID: 178852
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详细
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.
作者简介
I. Blatov
Volga State University of Telecommunications and Informatics
编辑信件的主要联系方式.
Email: blatow@mail.ru
俄罗斯联邦, Samara, 443090
A. Zadorin
Sobolev Institute of Mathematics (Omsk Branch), Siberian Branch
编辑信件的主要联系方式.
Email: zadorin@ofim.oscsbras.ru
俄罗斯联邦, Omsk, 644043
E. Kitaeva
Samara State University
Email: zadorin@ofim.oscsbras.ru
俄罗斯联邦, Samara, 443086
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