Numerical convergence of a Telegraph Predator-Prey system

Kariston Stevan Luiz; Juniormar Organista; Eliandro Rodrigues Cirilo; Neyva Maria Lopes Romeiro; Paulo Laerte Natti

doi:10.5433/1679-0375.2022v43n1Espp51

Numerical convergence of a Telegraph Predator-Prey system

Authors

Kariston Stevan Luiz Londrina State University - UEL https://orcid.org/0000-0002-4904-144X
Juniormar Organista University of São Paulo - USP - São Carlos https://orcid.org/0000-0002-3627-6901
Eliandro Rodrigues Cirilo Londrina State University - UEL https://orcid.org/0000-0001-7530-1770
Neyva Maria Lopes Romeiro Londrina State University - UEL https://orcid.org/0000-0002-3249-3490
Paulo Laerte Natti Londrina State University - UEL https://orcid.org/0000-0002-5988-2621

DOI:

https://doi.org/10.5433/1679-0375.2022v43n1Espp51

Keywords:

Reactive-Diffusive-Telegraph system, Maxwell-Cattaneo delay, discretization consistency, Von Neumann stability, numerical experimentation

Abstract

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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Author Biographies

Kariston Stevan Luiz, Londrina State University - UEL

Master by the Program of Applied and Computational Mathematics-PGMAC/UEL

Juniormar Organista, University of São Paulo - USP - São Carlos

PhD student in Applied Mathematics from ICMC-USP. Master by the Program of Applied and Computational Mathematics-PGMAC/UEL

Eliandro Rodrigues Cirilo, Londrina State University - UEL

Prof. Dr., Mathematics Depto., UEL, Londrina, PR, Brazil

Neyva Maria Lopes Romeiro, Londrina State University - UEL

Prof. Dr., Mathematics Depto., UEL, Londrina, PR, Brazil.

Paulo Laerte Natti, Londrina State University - UEL

Prof. Dr., Department of Mathematics, UEL, Londrina, PR, Brazil

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