Discrete superconvergent degenerate kernel method for Fredholm integral equations

C. Allouch, A. Boujraf and M. Tahrichi

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 164, issue C, 24-32

Abstract: Approximate solutions of integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we propose the discrete version of the superconvergent degenerate kernel method for solving Fredholm integral equation of the second kind with a smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain optimal convergence rates for both approximated solution and iterated discrete solution. Numerical results are presented to illustrate the theoretical estimates for the error of this method.

Keywords: Degenerate kernel method; Interpolatory projection; Gauss points; Nyström approximation (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:164:y:2019:i:c:p:24-32

DOI: 10.1016/j.matcom.2018.08.014

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