The development of simulation tools is becoming an important area in industry, recently fostered by the tremendous improvements in computer hardware. Many physical problems can be simulated by being modelled by mathematical equations which can then be solved numerically. This thesis is concerned with the development of a Finite Difference solver for time dependent partial differential equations. The development involves a number of challenging requirements that the solver must meet: to have the capacity of solving conservation and non-conservation laws (using several numerical techniques), to be robust, efficient and to have a modular and extendible design. Firstly, we focus on the architecture of the program and how an original design approach was used in order to carry out its development. A combination of Object- Oriented Design and Structured Design was adopted.