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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/4/386 |
| _version_ | 1827589165155352576 |
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| author | Michael John Baines Katerina Christou |
| author_facet | Michael John Baines Katerina Christou |
| author_sort | Michael John Baines |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-09T00:51:45Z |
| format | Article |
| id | doaj.art-a3159348ac1c4894aca1e1373f0d0fb5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T00:51:45Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a3159348ac1c4894aca1e1373f0d0fb52023-12-11T17:10:29ZengMDPI AGMathematics2227-73902021-02-019438610.3390/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 |
| 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 |
| title | 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_short | 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 |
| topic | segregation competition interface condition velocity-based moving meshes finite-differences |
| url | https://www.mdpi.com/2227-7390/9/4/386 |
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