Numerical solution of a hypersingular integral equation arising in a solid circular plate problem

A purely flexural mechanical analysis has been carried out for a thin, solid, circular plate deflected by a static transverse central force and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. Monegato and Strozzi [6,7] have considered two particular contact reactions: the case where only a distributed force takes place, and the situation in which a distributed force is jointed to a distributed couple of properly selected profile. Both of these problems can been formulated in terms of an integral equation of the Prandtl type with Hilbert and Volterra operators, associated with two constraints conditions. 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 \cite{CCJL}. The aim of the present paper is to present an algorithm related to the cited numerical model based on the collocation methods with quadrature methods on orthogonal polynomials as in \cite{CCJ,CCJL}. The optimal convergence rates presented here generalize the results shown in [7].