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This article is cited in 6 scientific papers (total in 6 papers)
About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer
I. A. Blatova, A. I. Zadorinb, E. V. Kitaevac a Volga region state university of telecommunications and informatics, Moskovskoe shosse, 77, Samara, 443090, Russia
b Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, 630090, Russia
c Samara national research University named after academician S.P. Korolyov, Moskovskoe shosse, 34, Samara, 443086, Russia
Abstract:
A problem of the Subbotin parabolic spline-interpolation of functions with large gradients in the boundary layer is considered. In the case of a uniform grid it has been proved and in the case of the Shishkin grid it has been experimentally shown that with a parabolic spline-interpolation of functions with large gradients the error in the exponential boundary layer can unrestrictedly increase with a fixed number of grid nodes. A modified parabolic spline has been constructed. Estimates of the interpolation error of the constructed spline don't depend from a small parameter.
Key words:
singular perturbation, boundary layer, Shishkin mesh, parabolic spline, modification, estimation of error.
Received: 27.06.2016 Revised: 08.11.2016
Citation:
I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer”, Sib. Zh. Vychisl. Mat., 20:2 (2017), 131–144; Num. Anal. Appl., 10:2 (2017), 108–119
Linking options:
https://www.mathnet.ru/eng/sjvm641 https://www.mathnet.ru/eng/sjvm/v20/i2/p131
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Abstract page: | 257 | Full-text PDF : | 38 | References: | 44 | First page: | 15 |
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