My research interest includes the development of the numerical methods for the singularly perturbed boundary value problems arising in many applications of science and engineering. Singularly perturbed boundary value problems are those in which the highest order derivative is multiplied by a small parameter ε, known as the perturbation parameter. As ε → 0, the order of the differential equation reduces by at least one and so the solution to the reduced problem fails to satisfy all the boundary conditions. Thus as ε → 0, the solution to these problems has multiple behaviors in the sense that there are the regions where solution changes very rapidly (these regions are called layer regions) otherwise the solution varies slowly (these regions are called outer regions). The classical/standard numerical methods fail to approximate the solution to these problems, so we need to develop non-classical/nonstandard methods for the solution of these problems.

In particular, my research includes the development of the numerical methods for Initial/Boundary Value Problems for Ordinary Differential Equations, Partial Differential Equations, Delay/Advanced Differential Equations, Singularly Perturbed ODEs/PDEs, Fractional Order ODEs/PDEs etc.