A Nystrom flavored Calder\'on Calculus of order three for two dimensional waves

In this paper we present and test a full discretization of all elements of the Calder\'on Calculus (layer potentials and integral operators) for the Helmholtz equation in smooth closed curves in the plane. The resulting integral equations provide approximations of order three for all variables involved. Test are shown for a wide array of direct, indirect and combined field integral equation at fixed frequency and for a Convolution Quadrature based approximation in the time domain.