A meshless numerical method for a system with intraspecific and interspecific competition



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Aquino, M. and Negreanu Pruna, Mihaela and Vargas, A.M. (2022) A meshless numerical method for a system with intraspecific and interspecific competition. Engineering Analysis with Boundary Elements, 145 . pp. 242-257. ISSN 0955-7997

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Official URL: https://doi.org/10.1016/j.enganabound.2022.09.005


In this paper we study a novel mathematical model with intraspecific and interspecific competition between two species consisting of a non-linear parabolic–ODE–parabolic system. It describes the evolution of two populations in competition for a resource, one of which is subject to chemotaxis. We analyze the local stability of the constant equilibrium solutions and we obtain the periodic behavior of the solution for certain data of the problem. For this purpose, we apply the meshless numerical method of Generalized Finite Differences (GFDM) and we prove the conditional convergence of the discrete solution to the analytical one. The conditional convergence of the numerical method is demonstrated and, thought its implementation, we obtain numerical solutions whose asymptotic behavior agrees with the analytically one expected. We give several numerical examples on the applications of this meshless method over regularly and irregularly distributed nodes to illustrate its potential.

Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Chemotaxis, Numerical methods, Asymptotic behavior, Competition
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:75787
Deposited On:28 Nov 2022 09:56
Last Modified:28 Nov 2022 10:00

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