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

[1306.0707] Convergence Analysis of a Numerical Algorithm for Spatial Segregation of Two Population Densities Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:1306.0707 (math) [Submitted on 4 Jun 2013 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: Convergence Analysis of a Numerical Algorithm for Spatial Segregation of Two Population Densities Authors: Avetik Arakelyan View PDF HTML (experimental) 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 $f_i(x)\geq 0$. At the end of the paper, we present computational tests. Comments: 16 pages, 8 figures, Keywords: Free boundary, Two-phase membrane problem, Reaction-diffusion systems, Finite difference Subjects: Numerical Analysis (math.NA) Cite as: arXiv:1306.0707 [math.NA] (or arXiv:1306.0707v3 [math.NA] for this version) https://doi.org/10.48550/arXiv.1306.0707 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Avetik Arakelyan Ara [ view email ] [v1] Tue, 4 Jun 2013 09:14:23 UTC (207 KB) [v2] Wed, 9 Dec 2015 19:52:22 UTC (206 KB) [v3] Thu, 27 Aug 2026 10:19:04 UTC (513 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2013-06 Change to browse by: cs cs.NA math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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