American Institute of Mathematical Sciences

2015, 12(2): 233-258. doi: 10.3934/mbe.2015.12.233

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

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

Received  April 2014 Revised  September 2014 Published  December 2014

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.
Citation: Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 233-258. doi: 10.3934/mbe.2015.12.233
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