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In this paper, we study a numerical approximation Free Boundary Problem (FBP) of a system of differential equations of nonlinear one-dimensional parabolic type, associated with the evolution of the interface, which describes the regional partition of two groups of individuals in a same species interacting in a spatial limit to obtain their own habitat and that is a priori completely unknown. Taking into account the local dynamic of the system, the implicit finite difference scheme is used, obtaining a nonlinear algebraic system of equations in each time step. Finally, some simulations of the distribution of population density and the evolution of the free boundary are displayed according to the time in different scenarios, based on an algorithm proposed and implemented in MATLAB, this validates the mathematical model FBP. [ABSTRACT FROM AUTHOR]