The numerical solution of Cauchy singular integral equations with additional fixed singularities

TitleThe numerical solution of Cauchy singular integral equations with additional fixed singularities
Publication TypeJournal Article
Year of Publication2021
AuthorsDe Bonis, MC, Laurita, C
JournalDolomites Research Notes on Approximation
Volume14
Issue2
Pagination26-38
Date Published04/2021
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number20356803
Abstract

In this paper we propose a quadrature method for the numerical solution of Cauchy singular integral equations with additional fixed singularities. The unknown function is approximated by a weighted polynomial which is the solution of a finite dimensional equation obtained discretizing the involved integral operators by means of a Gauss-Jacobi quadrature rule. Stability and convergence results for the proposed procedure are proved. Moreover, we prove that the linear systems one has to solve, in order to determine the unknown coefficients of the approximate solutions, are well conditioned. The efficiency of the proposed method is shown through some numerical examples.

URLhttp://ijse.padovauniversitypress.it/2021/2/5
DOI10.14658/pupj-ijse-2021-2-5