Journal Article

Numerical approximations for an age‐structured model of a population dispersing in a spatially heterogeneous environment

Qingping Deng and Thomas G. Hallam

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 3, pages 247-268
Published in print September 2004 | ISSN: 1477-8599
Published online September 2004 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/21.3.247
Numerical approximations for an age‐structured model of a population dispersing in a spatially heterogeneous environment

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As ecological information on life history and habitat characteristics has become more sophisticated, models have become more realistic, and simulation methodology has become more important. The numerical analysis of simulation models, especially those of complex structured ecological systems, is generally lacking. The numerical analysis techniques developed here are to help form a systematic basis for a simulation theory for physiologically structured, individual‐based population models in a spatially heterogeneous habitat. The major thrust of this paper is to develop and analyse a finite‐difference–finite‐element numerical approximation scheme for a mathematical model of an age‐structured population dispersing in a bounded spatial environment in Rn. The numerical scheme applies a characteristic finite‐difference discretization for the time–age domain and a finite‐element discretization with numerical integral modifications for the spatial domain. The scheme not only provides optimal error estimates from the numerical analysis perspective but also produces biologically reasonable approximate solutions in that the solutions remain non‐negative. The existence and boundedness of the non‐negative approximate solution are shown, and the optimal error estimate is proved.

Keywords: finite element; finite difference; characteristic; convergence; error estimate; population; age‐structured; nonlinear; non‐local; discontinuous; degenerate; diffusion

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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