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

Abstract

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.

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Correspondence to I. A. Blatov.

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Original Russian Text © I.A. Blatov, A.I. Zadorin, E.V. Kitaeva, 2018, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2018, Vol. 58, No. 3, pp. 365–382.

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Blatov, I.A., Zadorin, A.I. & Kitaeva, E.V. On the Parameter-Uniform Convergence of Exponential Spline Interpolation in the Presence of a Boundary Layer. Comput. Math. and Math. Phys. 58, 348–363 (2018). https://doi.org/10.1134/S0965542518030028

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  • DOI: https://doi.org/10.1134/S0965542518030028

Keywords

  • singular perturbation
  • boundary layer
  • exponential spline
  • error estimate
  • uniform convergence