A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion

A moving-mesh finite-difference solution of a Lotka-Volterra competition-diffusion model of theoretical ecology is described in which the competition is sufficiently strong to spatially segregate the two populations, leading to a two-phase problem with a coupling condition at the moving interface. A...

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Main Authors:	Michael John Baines, Katerina Christou
Format:	Article
Language:	English
Published:	MDPI AG 2021-02-01
Series:	Mathematics
Subjects:	segregation competition interface condition velocity-based moving meshes finite-differences
Online Access:	https://www.mdpi.com/2227-7390/9/4/386

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spelling	doaj-a3159348ac1c4894aca1e1373f0d0fb52021-02-16T00:02:32ZengMDPI AGMathematics2227-73902021-02-01938638610.3390/math9040386A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-DiffusionMichael John Baines0Katerina Christou1Department of Mathematics and Statistics, School of Mathematical, Physical and Computational Sciences (SMPCS), Faculty of Science, University of Reading, Reading RG6 6AH, UKDepartment of Mathematics and Statistics, School of Mathematical, Physical and Computational Sciences (SMPCS), Faculty of Science, University of Reading, Reading RG6 6AH, UKA moving-mesh finite-difference solution of a Lotka-Volterra competition-diffusion model of theoretical ecology is described in which the competition is sufficiently strong to spatially segregate the two populations, leading to a two-phase problem with a coupling condition at the moving interface. A moving mesh approach preserves the identities of the two species in space and time, so that the parameters always refer to the correct population. The model is implemented numerically with a variety of parameter combinations, illustrating how the populations may evolve in time.https://www.mdpi.com/2227-7390/9/4/386segregationcompetitioninterface conditionvelocity-based moving meshesfinite-differences
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Michael John Baines Katerina Christou
spellingShingle	Michael John Baines Katerina Christou A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion Mathematics segregation competition interface condition velocity-based moving meshes finite-differences
author_facet	Michael John Baines Katerina Christou
author_sort	Michael John Baines
title	A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion
title_short	A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion
title_full	A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion
title_fullStr	A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion
title_full_unstemmed	A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion
title_sort	moving-mesh finite-difference method for segregated two-phase competition-diffusion
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2021-02-01
description	A moving-mesh finite-difference solution of a Lotka-Volterra competition-diffusion model of theoretical ecology is described in which the competition is sufficiently strong to spatially segregate the two populations, leading to a two-phase problem with a coupling condition at the moving interface. A moving mesh approach preserves the identities of the two species in space and time, so that the parameters always refer to the correct population. The model is implemented numerically with a variety of parameter combinations, illustrating how the populations may evolve in time.
topic	segregation competition interface condition velocity-based moving meshes finite-differences
url	https://www.mdpi.com/2227-7390/9/4/386
work_keys_str_mv	AT michaeljohnbaines amovingmeshfinitedifferencemethodforsegregatedtwophasecompetitiondiffusion AT katerinachristou amovingmeshfinitedifferencemethodforsegregatedtwophasecompetitiondiffusion AT michaeljohnbaines movingmeshfinitedifferencemethodforsegregatedtwophasecompetitiondiffusion AT katerinachristou movingmeshfinitedifferencemethodforsegregatedtwophasecompetitiondiffusion
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A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion

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