Numerical integration of autonomous and non-autonomous non-linear size-structured population models

We present an efficiency study for autonomous and non-autonomous non-linear size-structured population models. The study considers three numerical methods: a characteristics scheme, the Lax–Wendroff method and the box method, which are completely described in the paper. Five test problems are considered with diverse degree of complexity: non-trivial equilibrium, periodic solutions and diverse growth functions. The study of the efficiency takes into account the properties of the numerical schemes (such as the stability) and uses a multiple regression analysis to determine the constants of the leading terms of the corresponding global errors. We show how the tables of errors and cpu-times can be used to explain the meaning of the efficiency results. In addition, we present the convergence analysis of the box method.