Accurate numerical potential and field in razor-thin axisymmetric discs

We demonstrate the high accuracy of the density splitting method to compute the gravitational potential and field in the plane of razor-thin, axially symmetric discs, as preliminarily outlined in Pierens & Hure (2004). Because residual kernels in Poisson integrals are not C^infinity-class functions, we use a dynamical space mapping in order to increase the efficiency of advanced quadrature schemes. In terms of accuracy, results are better by orders of magnitude than for the classical FFT-methods.