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 uhl, given by the difference scheme, converges to the lth component ul, when the mesh size h tends to zero, provided ul∈C2(Ω), for every l=1,2,…,m. In particular, our proof provides convergence of a difference scheme for the multi-phase obstacle problem.