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

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Abstract

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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Angulo, O., López-Marcos, J. C., & López-Marcos, M. A. (2014). Analysis of an efficient integrator for a size-structured population model with a dynamical resource. In Computers and Mathematics with Applications (Vol. 68, pp. 941–961). Elsevier Ltd. https://doi.org/10.1016/j.camwa.2014.04.009

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