About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer
I.A. Blatov1, A.I. Zadorin2, E.V. Kitaeva3
1Volga region state university of telecommunications and informatics, Moskovskoe shosse, 77, Samara, Russia, 443090
2Sobolev Institute of Mathematics of Siberian Branch of Russian Academy of Sciences, Omsk department, Pevtsova, 13, Omsk, Russia, 644043
3Samara national research University named after academician S.P. Korolyov, Moskovskoe shosse, 34, Samara, Russia, 443086
Keywords: сингулярное возмущение, пограничный слой, сетка Шишкина, параболический сплайн, модификация, оценка погрешности, singular perturbation, boundary layer, Shishkin mesh, parabolic spline, modification, estimation of error
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.
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