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

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.

De Bonis M. C., Laurita C. (2021) "The numerical solution of Cauchy singular integral equations with additional fixed singularities " Dolomites Research Notes on Approximation, 14(2), 26-38. DOI: 10.14658/PUPJ-DRNA-2021-2-5  
Year of Publication
2021
Journal
Dolomites Research Notes on Approximation
Volume
14
Issue Number
2
Start Page
26
Last Page
38
Date Published
04/2021
ISSN Number
2035-6803
Serial Article Number
5
DOI
10.14658/PUPJ-DRNA-2021-2-5
Issue
Section
SpecialIssue