Mathematics

My research focuses on studying the numerical solutions for time-dependent hyperbolic partial differential equations. In particular, I am interested in designing robust, stable and accurate—central schemes, upwind schemes, and central-upwind schemes for the systems of time-dependent conservation laws. As such systems are highly non-linear in nature, discontinuities in the solutions can appear even for smooth initial conditions. Due to this, the solutions break down in the classical sense, and thus weak solutions are required to consider. Therefore, numerical algorithms play an important role in studying such systems. One can find numerous discretization frameworks in literature. Typically, the Finite Difference (FD), Finite Volume (FV), and Discontinuous Galerkin  (DG) based methods are often used to construct stable and robust higher-order schemes.