[Unusual date] Bivariate Spline Solution to Nonlinear Diffusive PDE and Its Biological Applications

Applied and Computational Mathematics Seminar
Friday, April 8, 2016 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Department of Mathematics, University of Georgia
Bivariate  splines are smooth piecewise polynomial functions defined on a triangulation of arbitrary polygon.  They are extremely useful for numerical solution of PDE, scattered data interpolation and fitting, statistical data analysis, and etc..   In this talk, I shall explain its new application to a biological study.  Mainly, I will explain how to use them to numerically solve a type of nonlinear diffusive time dependent PDE which arise from a biological study on the density of species over a region of interest. I apply our spline solution to simulate a real life study on malaria diseases in Bandiagara, Mali. Our numerical result show some similarity with the pattern from the biological study in2013 in a blind testing.  In addition, I shall explain how to use bivariate splines to numerically solve several systems of diffusive PDEs: e.g. predator-prey type, resource competing type and other type  systems.