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Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains
Juan B Gutierrez1, Ming-Jun Lai2, George Slavov2
1Institute of Bioinformatics, University of Georgia, United States; Department of Mathematics, University of Georgia, United States.
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.
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