Benito Muñoz, Juan J.García Hernández, Miguel ÁngelGavete Corvinos, Luis AntonioNegreanu, MihaelaUreña, FranciscoVargas Ureña, Antonio Manuel2024-12-172024-12-172020-05-27J.J. Benito, A. García, L. Gavete, M. Negreanu, F. Ureña, A.M. Vargas, Solving a chemotaxis–haptotaxis system in 2D using Generalized Finite Difference Method, Computers & Mathematics with Applications, Volume 80, Issue 5, 2020, Pages 762-777, ISSN 0898-1221, https://doi.org/10.1016/j.camwa.2020.05.0081873-7668https://doi.org/10.1016/j.camwa.2020.05.008https://hdl.handle.net/20.500.14468/24948This is an Accepted Manuscript of an article published by Elsevier in "Computers & Mathematics with Applications, 80, 5, 2020, Pages 762-777", available at: https://doi.org/10.1016/j.camwa.2020.05.008. (https://www.sciencedirect.com/science/article/pii/S0898122120302066) Este es el manuscrito aceptado del artículo publicado por Elsevier en "Computers & Mathematics with Applications 80, 5, 2020, Pages 762-777", disponible en línea: https://doi.org/10.1016/j.camwa.2020.05.008. (https://www.sciencedirect.com/science/article/pii/S0898122120302066)We study a mathematical model of cancer cell invasion of tissue (extracellular matrix) consisting of a system of reaction-diffusion-taxis partial differential equations which describes the interactions between cancer cells, the matrix degrading enzyme and the host tissue. We analyze the local stability of the constant equilibrium solutions to the chemotaxis-haptotaxis system, we derive a discretization of the system by means of the Generalized Finite Difference Method (GFDM) and we prove the convergence of the discrete solution to the analytical one. Also, we provide several numerical examples on the applications of this meshless method over regular and irregular domains.eninfo:eu-repo/semantics/openAccess12 Matemáticas::1206 Análisis numérico::1206.13 Ecuaciones diferenciales en derivadas parciales24 Ciencias de la Vida::2407 Biología celularartículoChemotaxis-haptotaxisGeneralized Finite DifferencesMeshless method