On the Parameter-Uniform Convergence of Exponential Spline Interpolation in the Presence of a Boundary Layer



The paper is concerned with the problem of generalized spline interpolation of functions having large-gradient regions. Splines of the class C2, represented on each interval of the grid by the sum of a second-degree polynomial and a boundary layer function, are considered. The existence and uniqueness of the interpolation L-spline are proven, and asymptotically exact two-sided error estimates for the class of functions with an exponential boundary layer are obtained. It is established that the cubic and parabolic interpolation splines are limiting for the solution of the given problem. The results of numerical experiments are presented.


singular perturbation boundary layer exponential spline error estimate uniform convergence 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Povolzhskiy State University of Telecommunications and InformaticsSamaraRussia
  2. 2.Sobolev Institute of Mathematics, Omsk Branch, Siberian BranchRussian Academy of SciencesOmskRussia
  3. 3.Samara State Aerospace UniversitySamaraRussia

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