Reduced Basis Approximation for a Spatial Lotka-Volterra Model
We construct a reduced basis approximation for the solution to a system of nonlinear partial differential equations describing the temporal evolution of two populations following the Lotka-Volterra law. The first population’s carrying capacity contains a free parameter varying in a compact set. The...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/1983 |
| _version_ | 1797484755791380480 |
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| author | Peter Rashkov |
| author_facet | Peter Rashkov |
| author_sort | Peter Rashkov |
| collection | DOAJ |
| description | We construct a reduced basis approximation for the solution to a system of nonlinear partial differential equations describing the temporal evolution of two populations following the Lotka-Volterra law. The first population’s carrying capacity contains a free parameter varying in a compact set. The reduced basis is constructed by two approaches: a proper orthogonal decomposition of a collection of solution snapshots and a greedy algorithm using an a posteriori error estimator. |
| first_indexed | 2024-03-09T23:09:00Z |
| format | Article |
| id | doaj.art-9b6a56bce65d49acbf1f64eb1c9b8c4a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:09:00Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9b6a56bce65d49acbf1f64eb1c9b8c4a2023-11-23T17:47:48ZengMDPI AGMathematics2227-73902022-06-011012198310.3390/math10121983Reduced Basis Approximation for a Spatial Lotka-Volterra ModelPeter Rashkov0Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, ul. Akademik Georgi Bonchev, Blok 8, 1113 Sofia, BulgariaWe construct a reduced basis approximation for the solution to a system of nonlinear partial differential equations describing the temporal evolution of two populations following the Lotka-Volterra law. The first population’s carrying capacity contains a free parameter varying in a compact set. The reduced basis is constructed by two approaches: a proper orthogonal decomposition of a collection of solution snapshots and a greedy algorithm using an a posteriori error estimator.https://www.mdpi.com/2227-7390/10/12/1983reduced basis methodnonlinear reaction-diffusion equationparametrised partial differential equation |
| spellingShingle | Peter Rashkov Reduced Basis Approximation for a Spatial Lotka-Volterra Model Mathematics reduced basis method nonlinear reaction-diffusion equation parametrised partial differential equation |
| title | Reduced Basis Approximation for a Spatial Lotka-Volterra Model |
| title_full | Reduced Basis Approximation for a Spatial Lotka-Volterra Model |
| title_fullStr | Reduced Basis Approximation for a Spatial Lotka-Volterra Model |
| title_full_unstemmed | Reduced Basis Approximation for a Spatial Lotka-Volterra Model |
| title_short | Reduced Basis Approximation for a Spatial Lotka-Volterra Model |
| title_sort | reduced basis approximation for a spatial lotka volterra model |
| topic | reduced basis method nonlinear reaction-diffusion equation parametrised partial differential equation |
| url | https://www.mdpi.com/2227-7390/10/12/1983 |
| work_keys_str_mv | AT peterrashkov reducedbasisapproximationforaspatiallotkavolterramodel |