  Analytic methods show stability of the stationary accretion of test fluids
but they are inconclusive in the case of self-gravitating stationary flows. We
investigate numerically stability of those stationary flows onto compact
objects that are transonic and rich in gas. In all studied examples solutions
appear stable. Numerical investigation suggests also that the analogy between
sonic and event horizons holds for small perturbations of compact support but
fails in the case of finite perturbations.
