A polynomial collocation method for singular integro-differential equations in weighted spaces

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Author(s):	Rosa, M. A. ^[1] ; Cuminato, J. A. ^[1] ; McKee, S. ^[2] Total Authors: 3
Affiliation:	^[1] Univ Sao Paulo, Sao Carlos, SP - Brazil ^[2] Strathclyde Univ, Glasgow, Lanark - Scotland Total Affiliations: 2
Document type:	Journal article
Source:	Journal of Computational and Applied Mathematics; v. 368, APR 2020.
Web of Science Citations:	0
Abstract
A polynomial collocation method is proposed for the numerical solution of a class of singular integro-differential equations of Cauchy type; the collocation points are chosen to be the Chebyshev nodes. Function spaces are defined and theorems concerning the boundedness of certain operators are developed. Convergence of the numerical method is demonstrated in weighted uniform normed spaces of continuous functions; convergence rates are then determined in accordance with the smoothness of the functions characterizing the problem. Numerical examples are provided which go some way to confirming these estimates. (C) 2019 Elsevier B.V. All rights reserved. (AU)

FAPESP's process:	13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:	Francisco Louzada Neto
Support Opportunities:	Research Grants - Research, Innovation and Dissemination Centers - RIDC