Riv. Mat. Univ. Parma, Vol. 2, No. 1, 2011

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).


Home Riv.Mat.Univ.Parma