Numerical algorithms for a variational problem of the spatial segregation of reaction–diffusion systems

This paper is concerned with the numerical approximation of 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. The proposed numerical scheme is applied for the spatial segregation limit of diffusive Lotka–Volterra models in presence of high competition and inhomogeneous Dirichlet boundary conditions. The numerical implementations of the resulting approach are discussed and computational tests are presented.