title: Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.
abstract: We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems.
authors.affiliation: Institute of Bioinformatics, University of Georgia, United States; Department of Mathematics, University of Georgia, United States.
authors.forename: Juan B
authors.initials: JB
authors.lastname: Gutierrez
authors.affiliation: Department of Mathematics, University of Georgia, United States. Electronic address: mjlai@uga.edu.
authors.forename: Ming-Jun
authors.initials: MJ
authors.lastname: Lai
authors.affiliation: Department of Mathematics, University of Georgia, United States.
authors.forename: George
authors.initials: G
authors.lastname: Slavov
mesh_terms: D000818:Animals; D009033:Culicidae; D004199:Disease Vectors; D055669:Ecological and Environmental Phenomena; D008962:Models, Theoretical; D009032:Mosquito Control; D011156:Population Density
keywords: Allee effect; Bivariate splines; Ecology; Epidemiology; Numerical solution; PDE