On the convergence of the Generalized Finite Difference Method for solving a chemotaxis system with no chemical diffusion

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Benito, J. J. and García, A. and Gavete, L. and Negreanu, Mihaela and Ureña, F. and Vargas, A. M. (2021) On the convergence of the Generalized Finite Difference Method for solving a chemotaxis system with no chemical diffusion. Computational Particle Mechanics, 8 . pp. 625-636. ISSN 2196-4378

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Official URL: https://doi.org/10.1007/s40571-020-00359-w



Abstract

This paper focuses on the numerical analysis of a discrete version of a nonlinear reaction–diffusion system consisting of an ordinary equation coupled to a quasilinear parabolic PDE with a chemotactic term. The parabolic equation of the system describes the behavior of a biological species, while the ordinary equation defines the concentration of a chemical substance. The system also includes a logistic-like source, which limits the growth of the biological species and presents a time-periodic asymptotic behavior. We study the convergence of the explicit discrete scheme obtained by means of the generalized finite difference method and prove that the nonnegative numerical solutions in two-dimensional space preserve the asymptotic behavior of the continuous ones. Using different functions and long-time simulations, we illustrate the efficiency of the developed numerical algorithms in the sense of the convergence in space and in time.


Item Type:Article
Uncontrolled Keywords:Chemotaxis systems; Generalized Finite difference; Meshless method; Asymptotic stability
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:74749
Deposited On:23 Sep 2022 12:06
Last Modified:26 Sep 2022 07:37

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