Research Interests

My current research interest is in the numerical solution of spectral problems and ordinary differential equations, more specifically, the computation of eigenvalues of differential operators of Sturm-Liouville type and of more general forms. I  introduced two new techniques which are giving excellent results. The approaches introduced are based on the concepts of iterated integrals and Fliess series on the one hand and sampling theory on the other. Specifically I am considering,

• Singular Sturm-Liouville problems
• random Sturm-Liouville problems,
• vector Sturm-Liouville problems,
• non self-adjoint Sturm-Liouville problems
• non Local Sturm-Liouville problems
• fourth order Sturm-Liouville problems
• two parameter Sturm-Liouville problems
• multi-parameter Sturm-Liouville problems

I am also investigating

• Differential Equations on Time Scales, a recently introduced theory which bridges the gap between discrete and continuous analyses. In fact an M. Sc thesis titled “Impulsive differential equations on time scales” has been prepared (and defended) under my supervision.

• differential inclusions and their numerical solutions.
• Parallel computing using Message Passing Interface (MPI) and Parallel Virtual Machine (PVM)

• Nonlinear Systems. I have been working on their functional representation, stability and optimal control. I have introduced the idea of using the so-called Adomian Decomposition method in 1997.

• Impulsive Control