Supervisor: Dr. Taysir Dyhoum
A project on applying a variety of numerical techniques such as finite difference methods (FDM), finite difference method (FEM), boundary element method (BEM), and the method of fundamental solutions (MFS) that accurately approximate the solutions of a wide range of time/space-dependent or independent real-world problems, whether they are governed by linear or non-linear partial differential equations subject to various initial and boundary conditions. There is increasing demand for solutions to inverse problems, in which it is necessary to retrieve the equation coefficients (the medium properties) from information collected from the direct solver of the problem using the above numerical methods. The existence and uniqueness theorems for various inverse problems are also explored.