The study is a computational dynamic analysis which investigated the dynamics of fluid flow patterns in a homogeneous oil reservoir using the Radial Diffusivity Equation (RDE). The model was solved analytically for pressure using the Constant Terminal Rate Solution (CTRS) and numerically using the fully implicit Finite Difference Method (FDM). Results from the study indicated that the initial reservoir pressure would be able to do the extraction of oil for an extended period of time before any other recovery method would be used to aid in further extraction process depending on the rate at which oil is produced. The study further confirmed that reservoir simulation describing a radial flow of a compressible fluid in porous media may be adequately performed using ordinary laptop computers. It could be seen from the analysis of the plots of pressure vs. time, and space that the Pressure Transient Analysis (PTA) was duly followed. The approximate solutions of the analytical and numerical solutions to the model were in excellent agreement, thus the reservoir simulation model developed could be used to describe typical pressure-time relationships. The analytical solution was used to verify the numerical solution as an application. Overall, this study provides an improved platform for modeling single phase flow in oil and gas reservoirs.