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

Abstract

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 l h , given by the difference scheme, converges to the l th component u l , when the mesh size h tends to zero, provided u l ∈ C 2 (Ω), for every l = 1, 2, . . . , m. In particular, our proof provides convergence of a difference scheme for the multi-phase obstacle problem.2010 Mathematics Subject Classification. 35R35, 65N06, 65N22, 92D25.

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