Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model | Zendy

Azmy S. Ackleh | Zendy; Vinodh Chellamuthu | Zendy; Kazufumi Ito | Zendy

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Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model

Author(s) -

Azmy S. Ackleh,

Vinodh Chellamuthu,

Kazufumi Ito

Publication year - 2015

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2015.12.233

Subject(s) - measure (data warehouse) , mathematics , convergence (economics) , population model , finite difference , population , function (biology) , order (exchange) , scheme (mathematics) , mathematical optimization , finite difference method , computer science , mathematical analysis , demography , finance , evolutionary biology , sociology , economics , biology , economic growth , database

We study a quasilinear hierarchically size-structured population model presented in [4]. In this model the growth, mortality and reproduction rates are assumed to depend on a function of the population density. In [4] we showed that solutions to this model can become singular (measure-valued) in finite time even if all the individual parameters are smooth. Therefore, in this paper we develop a first order finite difference scheme to compute these measure-valued solutions. Convergence analysis for this method is provided. We also develop a high resolution second order scheme to compute the measure-valued solution of the model and perform a comparative study between the two schemes.

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