A quadrature method for Cauchy singular integral equations with singular given functions
Received: 30 March 2010
Accepted in revised form: 29 June 2010
Mathematics Subject Classification (2000): 65R20, 45E05.
Keywords: Cauchy singular integral equation.
Abstract: Cauchy singular integral equations with index zero and with singular given functions are investigated. In order to improve the smoothness properties of the known functions, following  (see also ), a regularizing procedure is introduced and a Cauchy singular integral equation with fixed singularities of Mellin convolution type is obtained. Thus a quadrature method is proposed whose stability and convergence is shown by means of numerical tests.
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