[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Ming-Jun Lai, University of Georgia
Abstract: 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..
I shall explain its new application to a biological study, how to use them to numerically solve a type of nonlinear diffusive time dependent partial differential equations which arise from some biological study on the density of species over a region of interest. In addition to some numerical validation of the spline solution, 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 in 2013 in a blind testing.
Finally I shall extend our study to numerically solve some systems of nonlinear diffusive PDEs: predator-prey type system, resource competing system, and other systems.