  A new discretization of the radial equations that appear in the solution of
separable second order partial differential equations with some rotational
symmetry (as the Schrodinger equation in a central potential) is presented. It
cures a pathology, related to the singular behaviour of the radial function at
the origin, that suffers in some cases the discretization of the second
derivative with respect to the radial coordinate. This pathology causes an
enormous slowing down of the convergence to the continuum limit when the two
point boundary value problem posed by the radial equation is solved as a
discrete matrix eigenvalue problem. The proposed discretization is a simple
solution to that problem. Some illustrative examples are discussed.
