**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