Semen Koksal

Title

Professor, Associate Department Head

Education

Ph.D., Florida Institute of Technology

Class Schedule

MTH 4320/5320 - Neural Networks - TR 3:30 - 4:45 pm

MTH 4201/5050 - Models in Applied Mathematics - MWF 9:00 - 9:50 am

MTH 4990 - Undergraduate Research - MW 1:30 - 3:00 pm

Office Hours

MW 10:00 - 11:00 am
TR 10:00 - 12:00 noon

Office

#313, Crawford Science Tower

Office Phone

321-674-8765

E-mail

skoksal@fit.edu

Website

Koksal's Home Page

Research Interests

  • Differential equations
  • linear algebra and geometry.

Research Areas

Dr. Knoll's research activities focus on mathematics education at the college level, particularly calculus instruction. Included in this is the integration of technology into the mathematics curriculum, placement testing (remediation) and teacher training, particularly graduate student assistants. Mathematical areas of interest include solutions to differential equations, linear algebra and geometry.

Current Research Projects

  • Nonlinear Differential Equations
  • Stability Analysis
  • Dynamical Systems
  • Numerical Analysis
  • Modeling and Mathematical biology.
  • Neural Networks

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 boundPedness 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. (Click here for the link)

Funded Projects

  • NSF Grant to conduct an interdisciplinary research on the mathematical modeling of coral bleaching.
  • UBM - Undergraduate training in Biology; Jan. 1, 2008, Dec. 31, 2010.

Selected Publications

  • M. Tezer-Sezgin and S. Köksal, "Finite element method for solving MHD flow in a rectangular duct", Int. J. Numerical Methods in Engineering, Vol.28(1989), pp.445-459.
  • S. Köksal, "Boundedness properties and perturbing Lyapunov functions", JMAA, Vol.163, No.1(1992), pp. 73-78.
  • S. Köksal and S. Sivasundaram, "Stability properties of the Hopfield type neural networks", Dynam. Stability Systems, 8(3) (1993), pp. 181-187.
  • S. Köksal and V. Lakshimikantham, "Generalized quasilinearization for nonlinear elliptic problems via nonvariational method", Nonlinear Studies, Vol.8, No.4(2001), pp.439-450.
  • S. Köksal and V. Lakshimikantham, "A unified monotone iterative technique for semilinear elliptic boundary value problems", Nonlinear Analysis, 51(2002), pp.567-586.
  • Abdullah Al-Namlah, Shirley A. Becker and S. Köksal, "Eliminating data duplication using a backprobagation neural net", Proc. Of Int. Conf. On Neural, Parallel, and Scientific Computations, Vol. 2 (2002), pp.37-43.
  • S. Köksal (with van Woesik R. and Lcharmoise, F.), "Annual Cycles of Solar Insolation Predict Spawning Times of Carribean Corals", Ecology Letters 9: 390-398 (2006).

Monographs

  • V. Lakshimikantham and S. Köksal, Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations, Francis and Taylor, 2003, London and New York.
  • S. Köksal (with van Woesik R.), A Coral Population Response (CPR) Model for Thermal Stress in COASTAL AND ESTRUARINE STUDIES: Coral Reefs and Climate Change Science and Management, American Geophysical Union, 2006.