Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model - Azmy S. Ackleh; Vinodh K. Chellamuthu; Kazufumi Ito (Mathematical Biosciences and Engineering)
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.