  Recently, much interest has gained the numerical approximation of equations
of the Spatial Segregation of Reaction-diffusion systems with m population
densities. These problems are governed by a minimization problem subject to the
closed but non-convex set. In the present work we deal with the numerical
approximation of equations of stationary states for a certain class of the
Spatial Segregation of Reaction-diffusion system with two population densities
having disjoint support. We prove the convergence of the numerical algorithm
for two competing populations with non-negative internal dynamics $f_i(x)\geq
0.$ At the end of the paper we present computational tests.
