Numerical methods for the Lotka–McKendrickʹs equation

The Lotka–McKendrickʹs model is a well-known model which describes the evolution in time of the age structure of a population. In this paper we consider this linear model and discuss a range of methods for its numerical solution. We take advantage of different analytical approaches to the system, to design different numerical methods and compare them with already existing algorithms. In particular we set up some algorithms inspired by the approach based on Volterra integral equations and we also consider a direct approach based on the nonlinear system that describes the evolution of the age profile of the population.