Fast numerical integration for simulation of structured population equations

In this paper, we consider the fast computation of integral terms arising in simulations of structured populations modeled by integro-differential equations. This is of enormous relevance for demographic studies in which populations are structured by a large number of variables (often called i-states) like age, gender, income etc. This holds equally for applications in ecology and biotechnology. In this paper we will concentrate on an example describing microbial growth. For this class of problems we apply the panel clustering method that has str almost linear complexity for many integral kernels that are of interest in the field of biology. We further present the primitive function method as an improved version of the panel clustering for the case that the kernel function is non-smooth on hypersurfaces. We compare these methods with a conventional numerical integration algorithm, all used in-side standard discretization schemes for the complete system of integro-differential equations.