RT Journal Article
T1 On the convergence of the Generalized Finite Difference Method for solving a chemotaxis systemwith no chemical diffusion
A1 Benito, J. J.
A1 García, A.
A1 Gavete, L.
A1 Negreanu, Mihaela
A1 Ureña, F.
A1 Vargas, A. M.
AB 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.
PB Springer
SN 2196-4378
YR 2021
FD 2021
LK https://hdl.handle.net/20.500.14352/7281
UL https://hdl.handle.net/20.500.14352/7281
LA eng
DS Docta Complutense
RD 16 may 2024