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Superconvergent Nyström method for Urysohn integral equations

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Abstract

Integral equations occur naturally in many fields of mechanics and mathematical physics. In this paper a superconvergent Nyström method has been used for solving one of the most important cases in nonlinear integral equations which is called Urysohn form. Using an interpolatory projection at the set of r Gauss points, it is shown that the proposed method has an order of 3r and one step of iteration improve the convergence order to 4r. The size of the nonlinear system of equations that must be solved to calculate the approximate solution using this method remains the same as the range of the interpolatory projection. Numerical results are given to illustrate the improvement of the order.

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Acknowledgments

We wish to express our great gratitude to the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Laboratoire LANO, FSO, URAC05, Université Mohammed 1er, Oujda, Maroc

    Driss Sbibih & Mohamed Tahrichi

  2. Laboratoire MASI-URAC05, Faculté de Nador, Université Mohammed 1er, Oujda, Maroc

    Chafik Allouch

Authors
  1. Chafik Allouch
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  2. Driss Sbibih
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  3. Mohamed Tahrichi
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Correspondence to Driss Sbibih.

Additional information

Communicated by Tom Lyche.

Research supported by URAC-05.

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Allouch, C., Sbibih, D. & Tahrichi, M. Superconvergent Nyström method for Urysohn integral equations. Bit Numer Math 57, 3–20 (2017). https://doi.org/10.1007/s10543-016-0629-6

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  • DOI: https://doi.org/10.1007/s10543-016-0629-6

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