I specialize in the study of Partial Differential Equations (PDEs) that emerge in various physical processes. My primary focus is on the development and analysis of numerical methods for solving PDEs, with a particular emphasis on scalar and systems of hyperbolic conservation laws. This broad classification encompasses the following areas:

• Numerical analysis and computational methods for Partial differntial equations
• Nonlinear system of hyperbolic conservation laws (A system of first order partial differential equations)
• Conservation laws with flux function allowed to be discontinuous in the space variable.
• High-order numerical methods for conservation laws.
• Discontinuous Galerkin methods for time-dependent partial differential equations.
• Polymer flooding problem in oil reservoir simulation.