Benito Muñoz, Juan J.García, ÁngelGavete, LuisNegreanu, MihaelaUreña, FranciscoVargas Ureña, Antonio Manuel2025-01-102025-01-102020-11J.J. Benito, A. García, L. Gavete, M. Negreanu, F. Ureña, A.M. Vargas (2020), Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method, Applied Numerical Mathematics Volume 157, Pages 356-371. doi: https://doi.org/10.1016/j.apnum.2020.06.0110168-9274https://doi.org/10.1016/j.apnum.2020.06.011https://hdl.handle.net/20.500.14468/25181This is a Submitted Manuscript of an article published by Elsevier in "Applied Numerical Mathematics Volume 157,Pages 356-371", available at: https://doi.org/10.1016/j.apnum.2020.06.011Este es el manuscrito enviado del artículo publicado por Elsevier en "Applied Numerical Mathematics Volume 157, Pages 356-371", disponible en línea: https://doi.org/10.1016/j.apnum.2020.06.011This 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.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículo