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Research Areas

Many phenomena in sciences, engineering, economics, and other areas are described by partial differential equations or PDEs. Exact (analytical) solutions of most of real world problems are often very difficult or impossible to obtain. Solutions to such problems can be approximated using numerical methods. At present, Numerical Methods for Solving Partial Differential Equations is a vast area which deals with numerical errors, stability, parallel algorithms, efficient computation, numerical solution of challenging multiphysics problems. I am carrying out research in the following areas of Numerical PDEs:

• Numerical methods for interface problems
• Orthogonal spline collocation method
• Iterative methods for solving large systems of linear and nonlinear equations
• Numerical solution of nonlinear elliptic PDEs
• Numerical solution of non-self-adjoint or indefinite problems
• Multigrid/multilevel methods
• Domain decomposition methods