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

Domenico Mezzanotte, Donatella Occorsio and Maria Grazia Russo
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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
Maria Grazia Russo: Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy

Mathematics, 2021, vol. 9, issue 21, 1-18

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.

Keywords: Fredholm integral equations; Nyström methods; product integration rules; orthogonal polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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