A numerical method for nonlinear age-structured population models with finite maximum age

We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin–MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.