Numerical approximations for an age-structured model of a population dispersing in a spatially heterogeneous environment.
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.
The Institute for Environmental Modelling and Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996, USA. deng@math.utk.edu
Qingping
Q
Deng
Thomas G
TG
Hallam
D000818:Animals; D003198:Computer Simulation; D004777:Environment; D020342:Finite Element Analysis; D005399:Fishes / Q000254:growth & development*; D008954:Models, Biological; D011157:Population Dynamics