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., 2017, Volume 20, Number 2,Pages <nobr>131

This article is cited 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. Blatov^a, A. I. Zadorin^b, E. V. Kitaeva^c

^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.

UDC: 519.652

Received: 27.06.2016
Revised: 08.11.2016

DOI: 10.15372/SJNM20170202