A Nyström method for integral equations with fixed singularities of Mellin type in weighted Lp spaces

M.C. De Bonis and C. Laurita

Applied Mathematics and Computation, 2017, vol. 303, issue C, 55-69

Abstract: We consider integral equations of the second kind with fixed singularities of Mellin type. According to the behavior of the Mellin kernel, we first determine suitable weighted Lp spaces where we look for the solution. Then, for its approximation, we propose a numerical method of Nyström type based on a Gauss–Jacobi quadratura formula. Actually, a slight modification of the classical procedure is introduced in order to prove convergence results in weighted Lp spaces. Moreover, a preconditioning technique allows us to solve well conditioned linear systems. We show the efficiency of the proposed method through some numerical tests.

Keywords: Mellin kernel; Integral equation of Mellin type; Nyström method; Lagrange interpolation; Gaussian rule (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:303:y:2017:i:c:p:55-69

DOI: 10.1016/j.amc.2017.01.027

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