Bisymmetric normal modes in soft-centred and realistic galactic discs
  We test methods for the determination of unstable modes in stellar discs: a
point collocation scheme in the action sub-space, a scheme based on expansion
of the density and potential on the biorthonormal basis, and a finite element
method. Using models of galaxies with low and high mass concentration to the
center, the existence of two different kinds of spectra of unstable modes is
demonstrated. Characteristic features of methods and obtained spectra are
discussed.
  Despite ignoring any constraint on the continuity or differentiability of the
perturbed DF, the collocation scheme is reliable for obtaining spectra and
patterns in both kinds of models. The method based on the expansion of the
perturbed potential and surface density over a biorthogonal basis was not
applicable to a model with high mass concentration. The finite element method
successfully used in various fields of science and engineering is currently
sensitive to the presence of resonant orbits due to the choice of interpolation
functions for the distribution function.
