Computing the eigenvalues of Gurtin-MacCamy models with diffusion

Abstract

We address numerically the question of the asymptotic stability of equilibria for a Gurtin–MacCamy model with age-dependent spatial diffusion. The problem reduces to the study of a finite number of simpler models without diffusion, which are parametrized by the eigenvalues of the Laplacian operator. Here the approach in Breda et al. (2007, Stability analysis of age-structured population equations by pseudospectral differencing methods. J. Math. Biol., 54, 701–720; 2008, Stability analysis of the Gurtin–MacCamy model. SIAM J. Numer. Anal., 46, 980–995), which is based on pseudospectral methods, is adapted to the reduced models and the error analysis is revisited in order to prove the preservation of convergence of infinite order.