Flores, JesúsGarcía, ÁngelNegreanu, M.Salete Casino, EduardoUreña, FranciscoA.M. Vargas2024-09-272024-09-272023J. Flores, A. García, M. Negreanu, E. Salete, F. Ureña, A.M. Vargas, A spatio-temporal fully meshless method for hyperbolic PDEs, Journal of Computational and Applied Mathematics, Volume 430, 2023, 115194, ISSN 0377-0427, https://doi.org/10.1016/j.cam.2023.1151940377-0427https://doi.org/10.1016/j.cam.2023.115194https://hdl.handle.net/20.500.14468/23841This is the Accepted Manuscript of an article published by Elsevier in "Journal of Computational and Applied Mathematics" on 2023, available online: https://doi.org/10.1016/j.cam.2023.115194 Este es el manuscrito aceptado de un artículo publicado por Elsevier en "Journal of Computational and Applied Mathematics" en 2023, disponible en línea: https://doi.org/10.1016/j.cam.2023.115194We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear hyperbolic PDEs. The method is based on the moving least squares method, more precisely in the Generalized Finite Difference Method which allows us to select well-conditioned stars. Several 2D and 3D examples including the time variable are shown for both regular and irregular node distributions. The results are compared with explicit GFDM both in terms of errors and execution time.eninfo:eu-repo/semantics/openAccess33 Ciencias Tecnológicas::3305 Tecnología de la construcciónartículogeneralized finite difference methodmeshless methodHyperbolic Partial Differential Equations