Numerical convergence of a Telegraph Predator-Prey system
Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of eq...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Universidade Estadual de Londrina
2022-11-01
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| Series: | Semina: Ciências Exatas e Tecnológicas |
| Subjects: | |
| Online Access: | https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/46236 |
| _version_ | 1797951648928104448 |
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| author | Kariston Stevan Luiz Juniormar Organista Eliandro Rodrigues Cirilo Neyva Maria Lopes Romeiro Paulo Laerte Natti |
| author_facet | Kariston Stevan Luiz Juniormar Organista Eliandro Rodrigues Cirilo Neyva Maria Lopes Romeiro Paulo Laerte Natti |
| author_sort | Kariston Stevan Luiz |
| collection | DOAJ |
| description |
Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of equations in a time-explicit form and in a space-implicit form was obtained. The consistency of the Telegraph Predator-Prey system discretization was verified. Von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Delayed Telegraph system. On the other hand, for our Telegraph Predator-Prey system, it was not possible to obtain the von Neumann conditions analytically. In this context, numerical experiments were carried out and it was verified that the mesh refinement and the model parameters, reactive constants, diffusion coefficients and delay constants, determine the stability/instability conditions of the discretized equations. The results of numerical experiments were presented.
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| first_indexed | 2024-04-10T22:33:55Z |
| format | Article |
| id | doaj.art-539a2d22cad441448f8d4918c0e975e1 |
| institution | Directory Open Access Journal |
| issn | 1676-5451 1679-0375 |
| language | English |
| last_indexed | 2024-04-10T22:33:55Z |
| publishDate | 2022-11-01 |
| publisher | Universidade Estadual de Londrina |
| record_format | Article |
| series | Semina: Ciências Exatas e Tecnológicas |
| spelling | doaj.art-539a2d22cad441448f8d4918c0e975e12023-01-16T15:53:02ZengUniversidade Estadual de LondrinaSemina: Ciências Exatas e Tecnológicas1676-54511679-03752022-11-01431Esp10.5433/1679-0375.2022v43n1Espp51Numerical convergence of a Telegraph Predator-Prey systemKariston Stevan Luiz0Juniormar Organista1Eliandro Rodrigues Cirilo2Neyva Maria Lopes Romeiro3Paulo Laerte Natti4Londrina State University - UELUniversity of São Paulo – USP - São CarlosLondrina State University - UELLondrina State University - UELLondrina State University - UEL Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of equations in a time-explicit form and in a space-implicit form was obtained. The consistency of the Telegraph Predator-Prey system discretization was verified. Von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Delayed Telegraph system. On the other hand, for our Telegraph Predator-Prey system, it was not possible to obtain the von Neumann conditions analytically. In this context, numerical experiments were carried out and it was verified that the mesh refinement and the model parameters, reactive constants, diffusion coefficients and delay constants, determine the stability/instability conditions of the discretized equations. The results of numerical experiments were presented. https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/46236Reactive-Diffusive-Telegraph systemMaxwell-Cattaneo delaydiscretization consistencyVon Neumann stabilitynumerical experimentation |
| spellingShingle | Kariston Stevan Luiz Juniormar Organista Eliandro Rodrigues Cirilo Neyva Maria Lopes Romeiro Paulo Laerte Natti Numerical convergence of a Telegraph Predator-Prey system Semina: Ciências Exatas e Tecnológicas Reactive-Diffusive-Telegraph system Maxwell-Cattaneo delay discretization consistency Von Neumann stability numerical experimentation |
| title | Numerical convergence of a Telegraph Predator-Prey system |
| title_full | Numerical convergence of a Telegraph Predator-Prey system |
| title_fullStr | Numerical convergence of a Telegraph Predator-Prey system |
| title_full_unstemmed | Numerical convergence of a Telegraph Predator-Prey system |
| title_short | Numerical convergence of a Telegraph Predator-Prey system |
| title_sort | numerical convergence of a telegraph predator prey system |
| topic | Reactive-Diffusive-Telegraph system Maxwell-Cattaneo delay discretization consistency Von Neumann stability numerical experimentation |
| url | https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/46236 |
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