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

Foreword

With the advent and rapid development of high performance computing and communication (HPCC) and robust and efficient mathematical/numerical algorithms, computational simulation has rapidly emerged as an essential tool for engineering analysis and design environment. It has fundamentally changed the way the underlying principles of science and engineering are applied to research, design, and development. 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. A truly multidisciplinary conference on Differential Equations and Computational Simulation, biannually organized by the Department of Mathematics and Statistics and the NSF Engineering Research Center (NSF/ERC) at Mississippi State University (MSU), provides a joint forum where mathematicians, scientists, and engineers from industries, federal laboratories, and academia exchange research and development ideas. An overall goal for the series of conferences is to promote research and education in mathematical and computational analysis of theoretical and applied differential equations.The first three Mississippi State Conferences on Differential Equations and Computational Simulations were held March 19-20, 1993, April 7-8, 1995, and May 16-17, 1997. Special issues of the Journal of Applied Mathematics and Computation (65:1-3, 1994 and 89:1-3, 1998) and of the electronic Journal of Differential Equations (Conference-01, 1997) were dedicated to the reviewed papers presented during these conferences.

The technical success of the first three conferences has led to a traditional offering of these biannual conferences. The fourth Mississippi State Conference on Differential Equations and Computational Simulations took place May 21-22, 1999. More than 110 researchers attended the fourth conference. Invited principal lectures were

- Lawrence C. Evans, University of California, Berkeley,
*Homogenization of Hamilton-Jacobi PDE and Hamiltonian ODE* - Charbel Farhat, University of Colorado, Boulder,
*Conservation Laws for the Solution of Systems of Differential Equations Governing CFD Problems with Moving Grids, and Fluid/Structure Interaction Problems* - Irene Fonseca, Carnegie Mellon University,
*New Developments in Partial Differential Equations and in the Calculus of Variations: Applications to Problems in Materials Science* - Ahmed Noor, University of Virginia,
*Pathway to the Future of Simulation and Learning* - James Serrin, University of Minnesota,
*The Status of the Ground State Problem for Quasilinear Elliptic Operators* - Paul Waltman, Emory University,
*A Perturbation Theorem with Applications to a Model of the Diffusive Chemostat* - Mary Wheeler, University of Texas, Austin,
*Synthetic Environments for Modeling Subsurface Flows*

The papers 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. Applications pertinent to wind engineering and aerospace, automotive and space vehicle design and analysis were presented.
- Inverse Problems - Parameter identifications involving nonlinear systems and inverse scattering.

Department of Mathematics and Statistics.

Bharat Soni

Department of Aerospace Engineering

Mississippi State University.

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