Ph.D., University of Southwestern Louisiana, 1989
Phone: (850) 474-2857
Office Location: Bldg 4, Room 346
My research interests lie in differential and integral equations, nonlinear dynamical systems, and mathematical modeling. Where analytical solutions are not known for a given nonlinear system, we establish sufficient (and sometimes necessary) conditions for existence and uniqueness of the solution. We utilize comparison results that we also establish, to develop the monotone iterative technique, to produce approximate solutions for the system. This approach has successfully led to results for:
· First-order singular systems with boundary conditions;
· First-order rectangular systems with boundary values;
· Integrodifferential systems with singular coefficients;
· Delay differential systems (hereditary) with singular coefficient matrices;
· Controllability of hybrid impulsive integrodifferential systems;
· Eigenvalue problems.
Since our main approach utilizes a mathematical modeling framework that lends itself to numerical computations, validation and analysis, there are byproducts that have intrinsic value in their own rights. We are able to mathematically model a real-life situation in order to either predict its future behavior or to better understand it. Current creative projects include investigating issues of real-life import to include:
- Problems in aerospace and aviations such as true altitude modeling and automatic landing gear for aeroplanes;
- Supersonic gas flow and impulsive hereditary phenomena.
- Phosphorous diagenesis.
I also have interest in the design, implementation, and assessment of innovative academic programs in higher education.