Numerical integration of an age-structured population model with infinite life span

Abstract

The choice of age as a physiological parameter to structure a population and to describe its dynamics involves the election of the life-span. The analysis of an unbounded life-span age-structured population model is motivated because, not only new models continue to appear in this framework, but also it is required by the study of the asymptotic behaviour of its dynamics. The numerical integration of the corresponding model is usually performed in bounded domains through the truncation of the age life-span. Here, we propose a new numerical method that avoids the truncation of the unbounded age domain. It is completely analyzed and second order of convergence is established. We report some experiments to exhibit numerically the theoretical results and the behaviour of the problem in the simulation of the evolution of the Nicholson’s blowflies model.