title: Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model.
abstract: 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.
authors: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States. asa5773@louisiana.edu.
authors: Azmy S
authors: AS
authors: Ackleh
authors: Vinodh K
authors: VK
authors: Chellamuthu
authors: Kazufumi
authors: K
authors: Ito
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D020342:Finite Element Analysis; D006801:Humans; D015233:Models, Statistical; D011156:Population Density; D011157:Population Dynamics; D013997:Time Factors