A collocation method for a hypersingular boundary integral equation via trigonometric differentiation

Abstract

Revisiting the author's paper from 1995 on this topic, a fully discrete collocation method is proposed for the hypersingular integral equation arising from the double-layer approach for the solution of Neumann boundary value problems in two dimensions which is based on trigonometric differentiation to discretize the principal part of the hypersingular operator. Convergence in a Sobolev space setting is proven and the spectral convergence of the method is exhibited by numerical examples.