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Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods

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Abstract

For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nyström and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynomials of degree \(\le r - 1.\) We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4r in the interpolation at Gauss points can be improved to \(4r+2\). We illustrate the improvement of the order of convergence by numerical experiments.

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Authors and Affiliations

  1. University Mohammed I, MFN, Team of Modelling and Scientific Computing, Nador, Morocco

    C. Allouch

  2. University Mohammed I, FSO, ANO Laboratory, Oujda, Morocco

    D. Sbibih & M. Tahrichi

Authors
  1. C. Allouch
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  2. D. Sbibih
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  3. M. Tahrichi
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Correspondence to M. Tahrichi.

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Allouch, C., Sbibih, D. & Tahrichi, M. Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods. Afr. Mat. 30, 469–482 (2019). https://doi.org/10.1007/s13370-019-00660-9

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  • DOI: https://doi.org/10.1007/s13370-019-00660-9

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