Vol. 18 No. 8 (2026): Convergence Analysis of a Numerical Algorithm for Spatial Segregation of Two Population Densities

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  Convergence Analysis of a Numerical Algorithm for Spatial Segregation of Two Population Densities

  Avetik Arakelyan

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  Abstract

  Over the last few decades, the numerical approximation of spatial segregation equations for reaction-diffusion systems with $m$ population densities has gained significant interest. These problems are governed by a minimization problem subject to a closed but non-convex set. In the present work, we deal with the numerical approximation of equations of stationary states for a certain class of the spatial segregation of reaction-diffusion systems with two population densities having disjoint support. We prove the convergence of the numerical algorithm for two competing populations with non-negative internal dynamics $f_i(x)\geq 0$, $i=1,2$. At the end of the paper, we present computational tests.

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