Abstract
In the paper we carry out a complete analysis of several efficient numerical methods for the solution of boundary integral equations defined on a non-smooth boundary. In particular the solution of the Helmholtz equation in the exterior of a closed wedge is studied. The analytical behaviour of the solution of the resulting boundary integral equation (with a non-compact operator) near the wedge is investigated. Numerical analysis of the collocation and iterated collocation method for the problem is presented. Graded meshes are used to reflect the «singular» behaviour of the analytical solution, as well as the degree of the polynomial approximant, in order to yield results with «optimal convergence rates»
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