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A Quadrature Method for the Singular Integral Equation on Curves with Corner Points
Author(s) -
Buehring Kathrin
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941670104
Subject(s) - mathematics , quadrature (astronomy) , piecewise , tanh sinh quadrature , gauss–kronrod quadrature formula , mathematical analysis , clenshaw–curtis quadrature , nyström method , gauss–hermite quadrature , numerical integration , integral equation , gaussian quadrature , electrical engineering , engineering
This paper is concerned with a quadrature method for the approximate solution of the singular integral equationon the closed curve Γ with a finite number of corner points. Here and are piecewise continuous functions on Γ. We establish necessary and sufficient conditions for the stability of the quadrature method and, in addition, derive the convergence rates. For this we shall apply techniques similar to those used in the case where Γ is an interval (cf. [8]). The crucial point is a change of the variables depending on a parameter and a subsequent application of a simple quadrature rule on a uniform grid.