  In the current work we consider the numerical solutions of equations of
stationary states for a general class of the spatial segregation of
reaction-diffusion systems with $m\geq 2$ population densities. We introduce a
discrete multi-phase minimization problem related to the segregation problem,
which allows to prove the existence and uniqueness of the corresponding finite
difference scheme. Based on that scheme, we suggest an iterative algorithm and
show its consistency and stability. For the special case $m=2,$ we show that
the problem gives rise to the generalized version of the so-called two-phase
obstacle problem. In this particular case we introduce the notion of viscosity
solutions and prove convergence of the difference scheme to the unique
viscosity solution. At the end of the paper we present computational tests, for
different internal dynamics, and discuss numerical results.
