Analysis of an efficient integrator for a size-structured population model with a dynamical resource

In this paper, an efficient numerical method for the approximation of a nonlinear size-structured population model is presented. The nonlinearity of the model is given by dependency on the environment through the consumption of a dynamical resource. We analyse the properties of the numerical scheme...

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Published inComputers & mathematics with applications (1987) Vol. 68; no. 9; pp. 941 - 961
Main Authors Angulo, O, Lopez-Marcos, J C, Lopez-Marcos, MA
Format Journal Article
LanguageEnglish
Published 01.11.2014
Subjects
Approximation
Asymptotic properties
Convergence
Daphnia magna
Evolution
Freshwater
Mathematical analysis
Mathematical models
Nonlinearity
Steady state
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Summary:In this paper, an efficient numerical method for the approximation of a nonlinear size-structured population model is presented. The nonlinearity of the model is given by dependency on the environment through the consumption of a dynamical resource. We analyse the properties of the numerical scheme and optimal second-order convergence is derived. We report experiments with academical tests to demonstrate numerically the predicted accuracy of the scheme. The model is applied to solve a biological problem: the dynamics of an ectothermic population (the water flea, Daphnia magna). We analyse its long time evolution and describe the asymptotically stable steady states, both equilibria and limit cycles.
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ISSN:0898-1221
DOI:10.1016/j.camwa.2014.04.009