  In this paper, we study a numerical approximation for a class of stationary
states for reaction-diffusion system with m densities having disjoint support,
which are governed by a minimization problem. We use quantitative properties of
both solutions and free boundaries to derive our scheme. Furthermore, the proof
of convergence of the numerical method is given in some particular cases. We
also apply our numerical simulations for the spatial segregation limit of
diffusive Lotka-Volterra models in presence of high competition and
inhomogeneous Dirichlet boundary conditions. We discuss numerical
implementations of the resulting approach and present computational tests.
