Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Numerical solution of a singular integral equation with Cauchy kernel in the plane contact problem

Authors: M. R. Capobianco and G. Criscuolo
Journal: Quart. Appl. Math. 69 (2011), 79-89
MSC (2010): Primary 65R20; Secondary 41A05
DOI: https://doi.org/10.1090/S0033-569X-2010-01231-3
Published electronically: December 9, 2010
MathSciNet review: 2807978
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Abstract: This paper describes a collocation method for solving numerically a singular integral equation with Cauchy and Volterra operators, associated with a proper constraint condition. The numerical method is based on the transformation of the given integral problem into a hypersingular integral equation and then applying a collocation method to solve the latter equation. Convergence of the resulting method is then discussed, and optimal convergence rates for the collocation and discrete collocation methods are given in suitable weighted Sobolev spaces. Numerical examples are solved using the proposed numerical technique.

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M. R. Capobianco
Affiliation: Istituto per le Applicazioni del Calcolo “Mauro Picone" - CNR, Sezione di Napoli, Via Pietro Castellino 111, 80131 Napoli, Italy
Email: mariarosaria.capobianco@cnr.it

G. Criscuolo
Affiliation: Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Complesso Monte Sant’Angelo, Edificio T, Via Cintia, 80126 Napoli, Italy
Email: giuliana.criscuolo@unina.it

DOI: https://doi.org/10.1090/S0033-569X-2010-01231-3
Received by editor(s): July 15, 2009
Published electronically: December 9, 2010
Article copyright: © Copyright 2010 Brown University

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