  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.
