A Nyström method for mixed boundary value problems in domains with corners

In this paper we propose a new approach to the numerical solution of the mixed Dirichlet-Neumann boundary value problem for the Laplace equation in planar domains with piecewise smooth boundaries. We consider a perturbed BIE system associated to the problem and present a Nyström method for its numerical solution. As Mellin type integral operators are involved, we need to modify the method close to the corners in order to prove its stability and convergence. Some numerical tests are also given to show the efficiency of the method here described.