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

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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

   

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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Keywords finite-difference approximations; Hierarchically size-structured population model; measure-valuedsolutions; convergence analysis.

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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  • 2. YAN LIU, ZE-RONG HE, ON THE WELL-POSEDNESS OF A NONLINEAR HIERARCHICAL SIZE-STRUCTURED POPULATION MODEL, The ANZIAM Journal, 2017, 58, 3-4, 482, 10.1017/S1446181117000025
  • 3. Jedrzej Jablonski, Dariusz Wrzosek, Measure-valued solutions to size-structured population model of prey controlled by optimally foraging predator harvester., Mathematical Models and Methods in Applied Sciences, 2019, 10.1142/S0218202519500313

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Copyright Info: 2015, Azmy S. Ackleh, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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