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

1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010
2. Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205

Abstract

We study a quasilinear hierarchically size-structured population modelpresented in [4]. In this model the growth, mortality andreproduction rates are assumed to depend on a function of thepopulation density. In [4] we showed that solutions to thismodel can become singular (measure-valued) in finite time even ifall the individual parameters are smooth. Therefore, in this paperwe develop a first order finite difference scheme to compute thesemeasure-valued solutions. Convergence analysis for this method isprovided. We also develop a high resolution second order scheme tocompute the measure-valued solution of the model and perform a comparative study between thetwo schemes.
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Citation: Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model. Mathematical Biosciences and Engineering, 2015, 12(2): 233-258. doi: 10.3934/mbe.2015.12.233

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