Fast numerical integration for simulation of structured population equations

T. Fischer*, Dmitry Logashenko, M. Kirkilionis, G. Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1987-2012
Number of pages26
JournalMathematical Models and Methods in Applied Sciences
Issue number12
StatePublished - Dec 2006
Externally publishedYes

Bibliographical note

Funding Information:
We thank Odo Diekmann and Steffen Börm for helpful discussions and the unknown referees for valuable suggestions. T.F. was supported by DFG project Wi 1037/8-1. D.L. was supported by BMBF project under the contract No. 03-GIM1S1. M.K. was supported by SFB 412.


  • Cellular growth
  • Fast numerical integration
  • Structured populations

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


Dive into the research topics of 'Fast numerical integration for simulation of structured population equations'. Together they form a unique fingerprint.

Cite this