Professor, Department of Mathematical Sciences
Ph.D., Florida Institute of Technology, 1992
Website: Dr. Koksal's Website
Research Areas
My area of expertise is the theory and applications of nonlinear differential equations. My research work and interest for the last 15 years can be summarized as:
1. Numerical solutions of magneto-hydro dynamic equations using the finite element method (My earlier work).
2. Stability such as, uniform, asymptotic, exponential, eventual and practical, and boundedness properties of nonlinear ordinary differential equations by using Lyapunov's second method.
3. The method of generalized quasilinearization and monotone iterative technique. Both of these methods provide an approximation for the solutions of nonlinear differential equations (both ordinary and partial) by means of lower and upper solutions. The main difference between these techniques is that generalized quasilinearization produces rapid convergence, namely, quadratic convergence that is of great interest in applications.
4. Neural networks. I have investigated various stability properties of continuous Hopfield neural networks and Grossberg' competitive neural networks. Recently, I have been working on implementation of neural networks to some data base problems in computer science, and navigation and underwater sound recognition problems in ocean engineering. I am also interested in using neural networks in DNA and RNA research in life sciences.
5. Mathematical biology, a very recent research interest. I have been conducting research in theoretical marine ecology. An interdisciplinary project is continuing on the mathematical modeling of the coral bleaching problem in terms of nonlinear systems of ordinary and partial differential equations. This research also includes numerical solutions of the models and physical interpretations of the results, and computer simulations.
In addition to these research areas, I am very much interested in undergraduate mathematics education, curriculum development and research projects for undergraduates.