An improved explicit scheme for age-dependent population model with spatial diffusion
Galena Pelovska 11 Universitá degli Studi di Trento, via Sommarive 14, I-38050, Povo (Trento), Italy
Received by the editors September 2, 2007 and, in revised form, October 31, 2007.
In this work we present three age-structured models with spatial dependence. We introduce an improved explicit method, namely Super-Time-Stepping (STS) developed for parabolic problems and we use its modification for the numerical treatment of our models. We explain how the acceleration scheme can be adapted to the age-dependent models. We prove convergence of the method in case of Dirichlet boundary conditions and we demonstrate the accuracy and the efficiency of the Modified STS comparing it with other numerical algorithms of same or higher order, namely the explicit, fully implicit and Crank-Nicolson standard schemes.
AMS subject classifications: 35M10, 65N06, 65N12, 92B99
Key words: population dynamics; age-dependence; linear diffusion; linear and nonlinear models; finite difference method; numerical acceleration; modified super-time-stepping