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Recovering the past movement of a contaminant plume from measurements of its current values is a challenging problem in hydrology. Moreover, modeling the movement of a contaminant plume backwards is an ill-posed problem due to the unstable and non-unique nature of the resulting solution. Therefore, standard numerical methods become unstable, making it impossible to simulate existing contaminant transport models with reversed time. This paper presents two major contributions to solve the backward problem. Firstly, a stable and consistent numerical method based on an operator-splitting concept which is effective in tracking back the contaminant movement, and secondly, an optimal condition for the choice of mesh width that enables the error during computer simulation to stay within a reasonable bound. The numerical method was validated by introducing errors of varied strengths at the starting point and reconstructing the contaminant profiles backwards at any given time. [ABSTRACT FROM AUTHOR]