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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Finite difference approximations for a size-structured population model with distributed states in the recruitment
Author(s): Ackleh, Azmy S
Farkas, Jozsef Zoltan
Li, Xinyu
Ma, Baoling
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Keywords: continuous structured population models
distributed states-at-birth
finite difference approximations
convergence theory
existence and uniqueness of solutions
Issue Date: 2015
Date Deposited: 25-Aug-2015
Citation: Ackleh AS, Farkas JZ, Li X & Ma B (2015) Finite difference approximations for a size-structured population model with distributed states in the recruitment. Journal of Biological Dynamics, 9 (Supplement 1), pp. 2-31.
Abstract: We consider a size-structured population model where individuals may be recruited into the population at different sizes. First- and second-order finite difference schemes are developed to approximate the solution of the model. The convergence of the approximations to a unique weak solution is proved. We then show that as the distribution of the new recruits become concentrated at the smallest size, the weak solution of the distributed states-at-birth model converges to the weak solution of the classical Gurtin-McCamy-type size-structured model in the weak* topology. Numerical simulations are provided to demonstrate the achievement of the desired accuracy of the two methods for smooth solutions as well as the superior performance of the second-order method in resolving solution-discontinuities. Finally, we provide an example where supercritical Hopf-bifurcation occurs in the limiting single state-at-birth model and we apply the second-order numerical scheme to show that such bifurcation also occurs in the distributed model.
DOI Link: 10.1080/17513758.2014.923117
Rights: © 2014 The Author(s). Published by Taylor & Francis. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The moral rights of the named author(s) have been asserted. Permission is granted subject to the terms of the License under which the work was published. Please check the License conditions for the work which you wish to reuse. Full and appropriate attribution must be given. This permission does not cover any third party copyrighted material which may appear in the work requested.
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