On the numerical solution of a hypersingular integral equation in scattering theory

We describe a fully discrete method for the numerical solution of the hypersingular integral equation arising from the combined double- and single-layer approach for the solution of the exterior Neumann problem for the two-dimensional Helmholtz equation in smooth domains. We develop an error analysis in a Hِlder space setting with pointwise estimates and prove an exponential convergence rate for analytic boundaries and boundary data.