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A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant

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Abstract

In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI) defined on a uniform criss-cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan’s iterated version and we illustrate the theoretical results by some numerical examples.

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Authors and Affiliations

  1. ESTO, Laboratoire MATSI, Equipe ANTI-URAC05, Université Mohammed I, Oujda, Morocco

    Chafik Allouch & Driss Sbibih

  2. INSA de Rennes, Centre de Mathématiques, Rennes, France

    Paul Sablonnière

Authors
  1. Chafik Allouch
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  2. Paul Sablonnière
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  3. Driss Sbibih
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Correspondence to Driss Sbibih.

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Research supported by URAC-05.

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Allouch, C., Sablonnière, P. & Sbibih, D. A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant. Numer Algor 62, 445–468 (2013). https://doi.org/10.1007/s11075-012-9598-2

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  • DOI: https://doi.org/10.1007/s11075-012-9598-2

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