In this paper we propose a numerical scheme to investigate the stability of steady
states of the nonlinear Gurtin–MacCamy system, which is a basic model in population dynamics.
In fact the analysis of stability is usually performed by the study of transcendental characteristic
equations that are too difficult to approach by analytical methods. The method is based on the
discretization of the infinitesimal generator associated to the semigroup of the solution operator by
using pseudospectral differencing techniques. The method computes the rightmost characteristic
roots, and it is shown to converge with spectral accuracy behavior.
