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arXiv · 1608.02188

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

Avetik Arakelyan
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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 $m\geq 2$ components. More precisely, we show that the numerical solution $u_h^l$, given by the difference scheme, converges to the $l^{th}$ component $u_l,$ when the mesh size $h$ tends to zero, provided $u_l\in C^2(\Omega),$ for every $l=1,2,\dots,m.$ In particular, our proof provides convergence of a difference scheme for the multi-phase obstacle problem.

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Avetik Arakelyan. 2016-08-07. Convergence of the finite difference scheme for a general class of the spatial segregation of reaction-diffusion systems. https://arxiv.org/abs/1608.02188

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