title: Finite difference approximations for a size-structured population model with distributed states in the recruitment.
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.
authors.affiliation: a Department of Mathematics , University of Louisiana at Lafayette , Lafayette , LA 70504 , USA.
authors.forename: Azmy S
authors.initials: AS
authors.lastname: Ackleh
authors.forename: József Z
authors.initials: JZ
authors.lastname: Farkas
authors.forename: Xinyu
authors.initials: X
authors.lastname: Li
authors.forename: Baoling
authors.initials: B
authors.lastname: Ma
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011156:Population Density; D011157:Population Dynamics; D015203:Reproducibility of Results
keywords: continuous structured population models; convergence theory; distributed states-at-birth; existence and uniqueness of solutions; finite difference approximations