Mathematics and Statistics Colloquium
Friday (2/23/2007) at 2:30pm in 304 Pickard Hall
"An Introduction to Nonstandard Finite Difference (NSFD) Schemes"Abstract: NSFD schemes provide techniques to eliminate particular types of numerical instabilities which can arise in the numerical integration of differential equations. We show, by imposing the condition of "dynamic consistency," that the NSFD methodology can generate schemes having superior numerical integration solutions as compared to standard procedures. We illustrate the application of NSFD methods by means of several examples from ordinary and partial differential equations. Various unresolved issues will also be presented.
For a full understanding of this presentation, only knowledge of the calculus and the basic concepts of differential equations are needed.
Ronald E. Mickens is the Distinguished Fuller E. Callaway Professor of Physics at Clark Atlanta University. He received his Ph.D. in theoretical physics from Vanderbilt University and has held postdoctoral positions at the Center for Theoretical Physics-MIT, The Joint Institute for Laboratory Astrophysics, and Vanderbilt University. His current research interests include nonlinear oscillations, difference equations, numerical integration of differential equations using nonstandard finite difference schemes, mathematical modeling of periodic diseases, and the history/sociology of African Americans in science. He has published more than 260 research papers, written six books, and edited eight volumes. Professor Mickens serves on the editorial boards of several research journals including the Journal of Difference Equations and Applications. His professional memberships include AAAS, the American Mathematical Society, the American Physical Society (for which he is an elected Fellow), and the Society for Mathematical Biology, and the History of Science Society.