%0 Journal Article
%A Benito, J. J.
%A García, A.
%A Gavete, L.
%A Negreanu, Mihaela
%A Ureña, F.
%A Vargas, A. M.
%T On the convergence of the Generalized Finite Difference Method for solving a chemotaxis systemwith no chemical diffusion
%D 2021
%@ 2196-4378
%U https://hdl.handle.net/20.500.14352/7281
%X 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.
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