Numerical integration methods for structured population models

The pseudospectral method has been widely used to study the properties of delay differential equations, renewal equations and partial differential equations via their reformulation as abstract differential equations. In this seminar we present its application to a reformulation, in terms of the integrated state, of a population model with two structuring variables described by a hyperbolic first-order PDE with integral boundary conditions. The novelty in the approach is that we use a change of variables that lets us integrate the state function along the characteristics. We are concerned with time-integration of the solutions to the model and, as we will see through some test examples, our approach appears promising in this regard.

This seminar concerns the results of Simone’s MSc thesis (advisor Rossana Vermiglio).