Numerical solution of a singular integral equation with Cauchy kernel in the plane contact problem

This paper describes a collocation method for solving numerically a singular integral equation with Cauchy and Volterra operators, associated with a proper constraint condition. The numerical method is based on the transformation of the given integral problem into a hypersingular integral equation and then applying a collocation method to solve the latter equation. Convergence of the resulting method is then discussed, and optimal convergence rates for the collocation and discrete collocation methods are given in suitable weighted Sobolev spaces. Numerical examples are solved using the proposed numerical technique.