A Variable Time Step Method for an Age-Dependent Population Model with Nonlinear Diffusion

Abstract

We propose a method for solving a model of age-dependent population diffusion with random dispersal. This method, unlike previous methods, allows for variable time steps and independent age and time discretizations. We use a moving age discretization that transforms the problem to a coupled system of parabolic equations. The system is then solved by backward differences in time and a Galerkin approximation in space; the equations that need to be solved at each step treat each age group separately. A priori L2 error estimates are obtained by an energy analysis. These estimates are superconvergent in the age variable. We present a postprocessing technique which capitalizes on the superconvergence.