Numerical integration of autonomous and non-autonomous non-linear size-structured population models.
We present an efficiency study for autonomous and non-autonomous non-linear size-structured population models. The study considers three numerical methods: a characteristics scheme, the Lax-Wendroff method and the box method, which are completely described in the paper. Five test problems are considered with diverse degree of complexity: non-trivial equilibrium, periodic solutions and diverse growth functions. The study of the efficiency takes into account the properties of the numerical schemes (such as the stability) and uses a multiple regression analysis to determine the constants of the leading terms of the corresponding global errors. We show how the tables of errors and cpu-times can be used to explain the meaning of the efficiency results. In addition, we present the convergence analysis of the box method.
Angulo
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Departamento de Matemática Aplicada a la Técnica, Escuela Universitaria Politécnica, Universidad de Valladolid, C/Fco. Mendizabal, no. 1, 47014 Valladolid, Spain. oscar@mat.uva.es
López-Marcos
J C
JC
D000818:Animals; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics; D013997:Time Factors