A Nyström Method for 2D Linear Fredholm Integral Equations on Curvilinear Domains

Anna Lucia Laguardia and Maria Grazia Russo ()
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Anna Lucia Laguardia: Department of Mathematics, Computer Science and Economics, University of Basilicata, Via dell’Ateneo Lucano 10, 85100 Potenza, Italy
Maria Grazia Russo: Department of Mathematics, Computer Science and Economics, University of Basilicata, Via dell’Ateneo Lucano 10, 85100 Potenza, Italy

Mathematics, 2023, vol. 11, issue 23, 1-17

Abstract: This paper is devoted to the numerical treatment of two-dimensional Fredholm integral equations, defined on general curvilinear domains of the plane. A Nyström method, based on a suitable Gauss-like cubature formula, recently proposed in the literature is proposed. The convergence, stability and good conditioning of the method are proved in suitable subspaces of continuous functions of Sobolev type. The cubature formula, on which the Nyström method is constructed, has an error that behaves like the best polynomial approximation of the integrand function. Consequently, it is also shown how the Nyström method inherits this property and, hence, the proposed numerical strategy is fast when the involved known functions are smooth. Some numerical examples illustrate the efficiency of the method, also in comparison with other methods known in the literature.

Keywords: Fredholm integral equations; Nyström method; polynomial approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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