Benito, J. J.García, A.Gavete, L.Negreanu Pruna, MihaelaUreña, F.Vargas, A. M.2023-06-172023-06-172020-07-020168-927410.1016/j.apnum.2020.06.011https://hdl.handle.net/20.500.14352/7280This work studies a parabolic-parabolic chemotactic PDE's system which describes the evolution of a biological population “U” and a chemical substance “V”, using a Generalized Finite Difference Method, in a two dimensional bounded domain with regular boundary. In a previous paper [12], the authors asserted global classical solvability and periodic asymptotic behavior for the continuous system in 2D. In this continuous work, a rigorous proof of the global classical solvability to the discretization of the model proposed in [12] is presented in two dimensional space. Numerical experiments concerning the convergence in space and in time, and long-time simulations are presented in order to illustrate the accuracy, efficiency and robustness of the developed numerical algorithms.engjournal articlehttps://doi.org/10.1016/j.apnum.2020.06.011open access519.6Generalized FiniteDifference Meshless methodChemotaxis systemAnálisis numérico1206 Análisis Numérico