Numerical  Partial Differential Equations:

Domain Decomposition

Methods of Lines

Adaptive methods

Mesh free approximation using Radial Bases Functions

Numerical methods for Stochastic Partial Differential Equations

Numerical methods for Multi scale Partial Differential Equations

Current Areas of Research

Computational Finance:

Pricing complex financial derivatives in high dimensions, Exotic Options, Jump Diffusion Models, American options with regime switching and transaction cost, Models with Stochastic Volatility, Parallel simulation of Binomial and Trinomial methods using MPI on Beowulf cluster, Numerical Methods for Estimating Risk Measures, Multi scale Modeling and simulation

Computational Bio Chemical Systems:

Large scale Reaction Diffusion equations, Complex Pattern Formation

Computational Stochastic Analysis:

Numerical analysis of Stochastic Partial Differential Equations.

Computational  Modeling in Biological Systems:

Proteins  Dynamics, Enzyme Kinetics, Chemotaxis, Multi-scale Modeling