Electronic Journal of Differential Equations, Conference 10, 2003.

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


With the rapid advancement in high performance computing and efficient numerical algorithms, mathematical modeling and computational simulations have become the third means, in addition to theory and experimentation, for scientific research. They have fundamentally changed the way the underlying principles of science and engineering are applied to research, design, and development. In many applications, mathematical modeling and computational simulations involve (i) system(s) of differential equations representing the scientific or engineering phenomena to be studied (mathematical model(s)); (ii) numerical methods used to calculate solutions to the mathematical model(s); and (iii) an efficient sequential/parallel/distributed computing environment. Because of the interdisciplinary nature of this process, a successful modeling and simulation effort requires close collaborations among mathematicians, computer scientists, and researchers in 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 this series of conferences is to promote research and education in mathematical and computational analyses of differential equations.

The first four Mississippi State Conferences on Differential Equations and Computational Simulations were held March 19-20, 1993, April 7-8, 1995, May 16-17, 1997, and May 21 – 22, 1999. 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 and Conference-03, 1999) were dedicated to the reviewed papers presented at these conferences.

The Fifth Mississippi State Conference on Differential Equations and Computational Simulations took place May 18 - 19, 2001. There were one hundred and thirty-eight participants from Japan, Germany, Brazil, Russia, Saudi Arabia and the United States registered for the conference. Invited principal lectures were

In addition, 69 contributed papers were presented during the two days of meetings. The conference also featured an honoring ceremony for Professor Jack Hale, a special lecture by Dr. Henry Warchall on the Funding Opportunities in the Mathematical Sciences at the NSF, and a Banquet Lecture titled "Highway to Space" by Dr. Gary Lyles. Professors Ratnasingham Shivaji and Bharat Soni served as conference organizers while Professor Jianping Zhu served as the Program Chair.

The papers in this special issue represent broad research in the following multidisciplinary areas:

  1. Mathematical Analysis and Bifurcation theory - Ordinary and partial differential equations involving reaction-diffusion, stability, and existence and uniqueness theories associated with initial and boundary value problems.
  2. 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.
  3. Computational Biology - Modeling of tumor growth, toxicity of mixtures of insecticides, and antibiotic penetration in biofilms.
We would like to thank the participants and principal speakers for their valuable contributions to the success of the conference and publication of the proceedings. We gratefully acknowledge the support provided by the National Science Foundation and the Institute for Mathematics and its Applications at University of Minnesota. We also acknowledge the support from the College of Arts and Sciences, the College of Engineering, the Office of Research, and the faculty and staff of the Department of Mathematics and Statistics and the NSF Engineering Research Center at Mississippi State University. Last but not least, we appreciate very much the diligence and responsiveness of the reviewers of the manuscripts that made the publication of this proceedings possible.

Special Issue Editors

John Graef
Department of Mathematics
University of Tennessee at Chattanooga

Rathasingham Shivaji
Department of Mathematics and Statistics
Mississippi State University

Bharat Soni
Department of Mechanical Engineering
University of Alabama at Birmingham

Jiangping Zhu
Department of Theoretical and Applied Mathematics
The University of Akron

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