LUISA FERMO
A quadrature method for Cauchy singular integral equations with singular given functions
Pages: 99-123
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 [29] (see also [31]), 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.
[29] G. Monegato, I. H. Sloan, Numerical solution of the generalized airfoil equation for an airfoil with a flap, SIAM J. Numer. Anal. 34 (1997), no. 6, 2288-2305.
[31] L. Scuderi, A collocation method for the generalized airfoil equation for an airfoil with a flap, SIAM J. Numer. Anal. 35 (1998), no. 5, 1725-1739 (electronic).