Numerical investigations of a class of biological models on unbounded domain

Abstract

This paper is concerned with numerical computations of a class of biological models on unbounded spatial domains. To overcome the unboundedness of spatial domain, we first construct efficient local absorbing boundary conditions (LABCs) to reformulate the Cauchy problem into an initial-boundary value (IBV) problem. After that, we construct a linearized finite difference scheme for the reduced IVB problem, and provide the corresponding error estimates and stability analysis. The delay-dependent dynamical properties on the Nicholson's blowflies equation and the Mackey-Glass equation are numerically investigated. Finally, numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.