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

Published: 01 April 2020 Publication History

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.

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Capobianco M.R., Junghanns P., Luther U., Matroianni G., Weighted uniform convergence of the quadrature method for Cauchy singular integral equations, in: Singular Integral Operators and Related Topics, in: Oper. Theory Adv. Appl., vol. 90, Birkhäuser Verlag, Basel, 1996, pp. 153–181.
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U. Luther, Uniform convergence of polynomial approximation methods for Prandtl’s integro-differential equation. Preprint 99-11, Dept. of Math. of the Techn. Univ. Chemnitz, 1999.
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            Published In

            cover image Journal of Computational and Applied Mathematics
            Journal of Computational and Applied Mathematics  Volume 368, Issue C
            Apr 2020
            742 pages

            Publisher

            Elsevier Science Publishers B. V.

            Netherlands

            Publication History

            Published: 01 April 2020

            Author Tags

            1. Cauchy singular integro-differential equations
            2. Polynomial collocation methods and convergence
            3. Weighted spaces of continuous functions

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