Nonstandard Finite Difference Schemes: Theory and Applications

4:15 PM-6:15 PM

*Room: Savannah 3*

The purpose of this minisymposium is to introduce the concept of "nonstandard" finite difference schemes and demonstrate their power and usefulness by applying these schemes to several problems involving nonlinear convection-diffusion-reactions, electromagnetics, and interacting population models of the Lotka-Volterra type. An important feature of these schemes is that they generally do not have many of the numerical instabilities which occur in using standard methods. Also, restrictions on the step-sizes are either eliminated or are weaker in comparison to conventional procedures. This often leads to significant savings in computational effort.

**Organizer: Ronald E. Mickens**

*Clark Atlanta University*

**4:15-4:40 Review of Nonstandard Finite Difference Methods**

- Ronald E. Mickens, Organizer

**4:45-5:10 Nonstandard Eulerian-Lagrangian Methods for Convection-Diffusion-Reaction Equations**

- Hristo V. Kojouharov, Arizona State University; and
*Benito M. Chen*, University of Wyoming

**5:15-5:40 Nonstandard Finite Differences and Physical Applications**

- James B. Cole, University of Tsukuba, Japan

**5:45-6:10 Nonstandard Discretization of Competitive and Cooperative Models**

- Saber Elaydi, Trinity University

*tjf, 1/19/99, MMD, 2/2/99*