In this paper a numerical scheme to investigate the stability of linear models of age-structured population dynamics is studied. The method is based on the discretization of the infinitesimal generator associated to the semigroup of the solution operator by using pseudospectral differencing techniques, hence following the approach recently proposed in Breda et al. [SIAM J Sci Comput
27(2): 482–495, 2005] for delay differential equations. The method computes the rightmost characteristic roots and it is shown to converge with spectral accuracy behavior.
