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 \(m\geq 2\) components. More precisely, we show that the numerical solution \(u_h^l\), given by the difference scheme,...

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Author: Arakelyan, Avetik
Format: Article
Language:English
Subjects:
Convergence
Finite difference method
Mathematical analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422