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.

On the numerical integration of non-local terms for age-structured population models.

We formulate explicit second-order finite difference schemes for the numerical integration of non-linear age-dependent population models. These methods have been designed by means of a representation formula for the theoretical solution of the integro-differential equation joint with open quadrature formulae for the numerical approximation of non-local terms. The schemes are analyzed and some numerical experiments are also reported in order to show numerically their accuracy.

Numerical schemes for size-structured population equations.

We formulate schemes for the numerical solution of size-dependent population models. Such schemes discretize size by means of a natural grid, which introduces a discrete dynamics. The schemes are analysed and optimal rates of convergence are derived. Some numerical experiments are also reported to demonstrate the predicted accuracy of the schemes.