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Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations

Author

Listed:
  • Abdelmonaim Saou

    (Team ANAA, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco)

  • Driss Sbibih

    (Team ANTO, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco)

  • Mohamed Tahrichi

    (Team ANAA, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco)

  • Domingo Barrera

    (Department of Applied Mathematics, University of Granada, Campus de Fuentenueva s/n, 18071 Granada, Spain)

Abstract

The aim of this paper is to carry out an improved analysis of the convergence of the Nyström and degenerate kernel methods and their superconvergent versions for the numerical solution of a class of linear Fredholm integro-differential equations of the second kind. By using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomial functions of degree ⩽ r − 1 , we obtain convergence order 2 r for degenerate kernel and Nyström methods, while, for the superconvergent and the iterated versions of theses methods, the obtained convergence orders are 3 r + 1 and 4 r , respectively. Moreover, we show that the optimal convergence order 4 r is restored at the partition knots for the approximate solutions. The obtained theoretical results are illustrated by some numerical examples.

Suggested Citation

  • Abdelmonaim Saou & Driss Sbibih & Mohamed Tahrichi & Domingo Barrera, 2022. "Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:893-:d:768803
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    References listed on IDEAS

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    1. M. Lakestani & M. Razzaghi & M. Dehghan, 2006. "Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-12, February.
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