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Groundwater flow problems can be expressed mathematically with the employ of partial differential equations and which could be solved analytically or numerically.  The results obtained showed that the direction of flow of groundwater is from a region of higher hydraulic head to a lower hydraulic head, and that pumping groundwater from the well faster than it is recharged leads to dry wells.  The numerical methods used for the analysis of Transient and steady-state groundwater flow produced efficient, effective and accurate solution and can be used for all real-life problems.