Finite difference methods are reasonably feasible for the solution of partial differential equations with initial and boundry conditions. One of the explicit methods being used in different techniques is Richardson's method. Here in this study a numerical example is taken and the same Richardson's method is applied using a different strategy, thus minimizing the discretization and local truncation error. An attempt has been made to compare the point SOR and Line SOR methods for that particular problem. These algorithms have been programmed in FORTRAN-77 and experimented interactively on the Honeywell MULTICS System of Loughborough University computer Centre, U. K.