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Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind

Author

Listed:
  • Domenico Mezzanotte

    (Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy)

  • Donatella Occorsio

    (Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy
    C.N.R. National Research Council of Italy, IAC Institute for Applied Computing “Mauro Picone”, Via P. Castellino 111, 80131 Napoli, Italy)

  • Maria Grazia Russo

    (Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy)

Abstract

In this paper, we propose a suitable combination of two different Nyström methods, both using the zeros of the same sequence of Jacobi polynomials, in order to approximate the solution of Fredholm integral equations on [ − 1 , 1 ] . The proposed procedure is cheaper than the Nyström scheme based on using only one of the described methods . Moreover, we can successfully manage functions with possible algebraic singularities at the endpoints and kernels with different pathologies. The error of the method is comparable with that of the best polynomial approximation in suitable spaces of functions, equipped with the weighted uniform norm. The convergence and the stability of the method are proved, and some numerical tests that confirm the theoretical estimates are given.

Suggested Citation

  • Domenico Mezzanotte & Donatella Occorsio & Maria Grazia Russo, 2021. "Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2652-:d:660625
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