On convergence of numerical algorithm of a class of the spatial segregation of reaction-diffusion system with two population densities

TL;DR

This paper investigates the convergence of a numerical algorithm for stationary states in a reaction-diffusion system modeling two competing populations with disjoint support, providing theoretical proof and computational validation.

Contribution

It introduces a convergent numerical method for a class of spatial segregation models with two populations, addressing non-convex minimization challenges.

Findings

Proved convergence of the numerical algorithm for the model.

Validated the method through computational tests.

Applicable to systems with non-negative internal dynamics.

Abstract

Recently, much interest has gained the numerical approximation of equations of the Spatial Segregation of Reaction-diffusion systems with m population densities. These problems are governed by a minimization problem subject to the 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 system with two population densities having disjoint support. We prove the convergence of the numerical algorithm for two competing populations with non-negative internal dynamics $f_i(x)\geq 0.$ At the end of the paper we present computational tests.