My research interest lies in the field of linear and nonlinear wave propagation. More specifically, my interest is in the study of partial differential equations of hyperbolic type. Most of the systems of PDEs (of practical interest) are not solvable exactly to get closed form solutions and therefore an approximation procedure needs to be adopted. Also, since the solution spaces of these systems are often vast (for instance the space of BV functions in the case of hyperbolic system of conservation laws), any qualitative analysis becomes more challenging. Because of the availability of powerful computational technology, numerical study of such problems attracted many researchers. However, in some practical applications, it is very expensive to go for full numerical simulations. Hence, in order to minimize the computational cost and/or to bring out some specific features of the solution, certain approximations of a governing system are in focus. My research focuses on developing some robust numerical methods and other methods based on nonlinear geometric theory, and their analysis.