Numerical solution of a class of singular integral equations

Capobianco, Criscuolo and Junghanns [2] have studied an integro differential equation of Prandtl type and a collocation method as well as a quadrature method for its approximate solution in weighted Sobolev spaces. Furthermore, collocation and collocation quadrature methods for the same integral equation have been studied in weighted spaces of continuous functions [3]. The aim of the present paper is to present an algorithm related to a numerical model for a hypersingular Integral equation arising in a solid circular plate problem, based on the collocation methods with quadrature methods on orthogonal polynomials as in [2, 3]. The optimal convergence rates is proved.