Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations

Foreword

With the advent and rapid development of super computers and high performance workstations, it is becoming possible to simulate complex scientific and engineering models by numerical solution of pertinent systems of differential equations. These computational simulations involve (i) a system of differential equations representative of the physical phenomena (mathematical model); (ii) a numerical method to simulate the mathematical models; and (iii) an efficient sequential/parallel/distributed computing environment requiring an interdisciplinary collaboration between various scientific and engineering fields. In this view, a truly multidisciplinary conference on Differential Equations and Computational Simulation has been initiated by the Department of Mathematics and Statistics and the NSF Engineering Research Center (NSF/ERC) at Mississippi State Universtiy (MSU). The primary objective of this series of conferences is to provide a joint forum where mathematicians, scientists and engineers from industries, federal laboratories and academia exchange research and development ideas. An overall goal for the conferences is to promote research and education in mathematical and computational analysis of theoretical and applied differential equations.
The first two Mississippi State Conferences on Differential Equations and
Computational Simulations were held March 19-20, 1993 and April 7-8, 1995.
Special issues of the journal of * Applied Mathematics and Computation
* (65:1-3, 1994 and 89:1-3, 1998) were dedicated to the reviewed papers
presented during these conferences.

Following the technical success of the first two conferences, the third Mississippi State Conference on Differential Equations and Computational Simulations took place May 16-17, 1997. The third conference was attended by more than 130 researchers. Invited principal lectures were presented by

- Walter Allegretto, University of Alberta, Canada:
*Microsensor Analysis and Simulation* - Jerry L. Bona, University of Texas:
*Stability and Instability of Solitary Waves and Associated Singularity Formation* - Djairo de Figueiredo, University of Campinas, Brazil:
*Decay, Symmetry and Existence of Positive Solutions of Semilinear Elliptic Systems* - S. Godunov, Sobolev Institute of Mathematics, Russia:
*Spectral Stratification in Models of Finite Elements for Elliptic Problems* - Antony Jameson, Princeton University:
*Optimum Aerodynamic Shape Design* - Jean Mawhin, Universite de Louvain, Belgium:
*Floquet Boundary Value Problems for Nonlinear Differential Equations: A Blend of Topology and Symmetry* - Stanley Osher, University of California:
*The Level Set Method: What's In It For You?* - Klaus Schmitt, University of Utah:
*Bifurcation Problems for Variational Inequalities* - Joseph Shang, Wright Patterson Air Force Base:
*High Resolution Schemes for Computational Electromagnetics in the Time Domain*

The papers in this proceedings represent research in the following multidisciplinary areas:

- Mathematical Development/Analysis-Bifurcation theory, ordinary and partial differential equations involving reaction-diffusion, stability, and existence and uniqueness theories associated with boundary value problems.
- Computational/Numerical Techniques - Computational fluid dynamic involving free surface flows and moving boundaries, grid generation and adaptive methods, and parallel algorithms.
- Inverse Problems - Parameter identifications involving nonlinear systems and inverse scattering.

We appreciate the diligence and responsiveness of the reviewers of the manuscripts. As this goes to press, the Fourth Conference on Differential Equations and Computatonal Simulations is planned for spring 1999 at MSU. It is our hope that the tradition of technical success of the first three conferences continues.

Department of Mathematics and Statistics.

Bharat Soni

Department of Aerospace Engineering

Mississippi State University.

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