language: en

[SIAM J. NUMER. ANAL. c 2000 Society for Industrial and Applied Mathematics Vol. 37, No. 5, pp. 1571?1589]

A VARIABLE TIME STEP METHOD FOR AN AGE-DEPENDENT POPULATION MODEL WITH NONLINEAR DIFFUSION

BRUCE P. AYATI

Abstract. We propose a method for solving a model of age-dependent population diusion 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 system of parabolic equations. The system is then solved by backward dierences 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 L 2 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.

Key words. population dynamics, age-dependence, nonlinear diusion, variable time steps, superconvergence, postprocessing. AMS subject classitcations. 35Q80, 65M06, 65M15, 65M60, 92D25. PII. S003614299733010X

1. Introduction.