Date: Friday, January 18, 2013
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: On nonstandard finite-difference schemes in biosciences
Abstract: Biological processes that arise in science are very complex. A lot of effort has been and is being made to build differential models that aim at elucidating these phenomena. However, these models cannot be completely solved by analytic techniques. Consequently, reliable numerical simulations are of fundamental importance in gaining some useful insights on the solutions of the differential equations. Of paramount importance for the involved dynamical systems is the design of numerical simulations that replicate their underlying dynamics such as the positivity of solutions, the dissipativity of the systems, the conservation laws, the stability of equilibria.
In this talk we design, analyze and implement nonstandard finite difference (NSFD) schemes for some differential models in biosciences. The NSFD schemes are reliable in three directions. They are topologically dynamically consistent for one-dimensional models. They can replicate the global asymptotic stability of the disease-free equilibrium of the MSEIR model in epidemiology whenever the basic reproduction number is less than 1. They preserve the positivity and boundedness property of solutions of advection-reaction and reaction-diffusion equations.
Speaker: Jean M.-S. Lubuma
Institution: University of Pretoria, South Africa
Event Organizer: Trace Jackson tjacks@umich.edu
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