Convergence of the finite difference scheme for a general class of the spatial segregation of reaction-diffusion systems

In this work we prove convergence of the finite difference scheme for equations of stationary states of a general class of the spatial segregation of reaction-diffusion systems with m >= 2 components. More precisely, we show that the numerical solution u(h)(l), given by the difference scheme, converges to the lth component u(l), when the mesh size h tends to zero, provided u(l) is an element of C-2 (Omega), for every l = 1, 2,...,m. In particular, our proof provides convergence of a difference scheme for the multi-phase obstacle problem. (C) 2018 Elsevier Ltd. All rights reserved.