Numerical methods on graded meshes for singular integral equations with conjugation

Issue title: Computational and Mathematical Methods for Science and Engineering Conference 2002 – CMMSE-2002

Article type: Research Article

Authors: Didenko, V.^{a; *} | Pittaluga, G.^b | Sacripante, L.^b | Venturino, E.^b

Affiliations: [a] Department of Mathematics, University of Brunei Darussalam, Brunei | [b] Dipartimento di Matematica, via Carlo Alberto 10, Universita' di Torino, 10123 Torino, Italy

Correspondence: [*] Corresponding author

Abstract: In this paper we consider simple methods for the numerical solution of Cauchy singular integral equations with conjugation based on quadratures. They use collocation at a set of nodes which is graded toward the endpoints, to accomodate for the presence of the singularity. Our numerical experience reveals that the theoretical stability findings are indeed of practical applicability, as the empirical condition number is seen very often to reach a plateau, whose asymptotic value is indeed very low.

DOI: 10.3233/JCM-2004-41-219

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 209-233, 2004