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Stability analysis of the Gurtin-MacCamy model. (English) Zbl 1159.92031
Summary: We propose a numerical scheme to investigate the stability of steady states of the nonlinear M. E. Gurtin and R. C. MacCamy system [Arch. Ration. Mech. Anal. 54, 281–300 (1974; Zbl 0286.92005)], 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.

MSC:
92D25Population dynamics (general)
65Q05Numerical methods for functional equations (MSC2000)
65J15Equations with nonlinear operators (numerical methods)
65J10Equations with linear operators (numerical methods)