Salete Casino, EduardoFlores, JesúsGarcía, ÁngelNegreanu, MihaelaVargas Ureña, Antonio ManuelUreña, Francisco2025-01-072025-01-072021-09-17Salete E, Flores J, García Á, Negreanu M, Vargas AM, Ureña F. Solving Eikonal equation in 2D and 3D by generalized finite difference method. Comp and Math Methods. 2021; 3(6):e1203. http://doi.org/https://doi.org/10.1002/cmm4.12032577-7408http://doi.org/https://doi.org/10.1002/cmm4.1203https://hdl.handle.net/20.500.14468/25121Este es el manuscrito aceptado del artículo. La versión registrada fue publicada por primera vez en Comp and Math Methods. 2021; 3(6):e1203., está disponible en línea en el sitio web del editor: http://doi.org/https://doi.org/10.1002/cmm4.1203 This is the accepted manuscript of the article. The registered version was first published in Comp and Math Methods. 2021; 3(6):e1203., is available online at the publisher's website: http://doi.org/https://doi.org/10.1002/cmm4.1203In this paper we propose an implementation, for irregular cloud of points, of the meshless method called Generalized Finite Di erence Method to solve the fully nonlinear Eikonal equation in 2D and 3D. We obtain the explicit formulae for derivatives and solve the system of nonlinear equations using the Newton-Raphson method to obtain the approximate numerical values of the function for the discretization of the domain. It is also shown that the approximation of the scheme used is of second order. Finally, we provide several examples of its application over irregular domains in order to test accuracy of the scheme, as well as comparison with order numerical methods.eninfo:eu-repo/semantics/openAccess33 Ciencias Tecnológicas::3310 Tecnología industrialartículoGeneralized finite difference methodnonlinear Eikonal equationMeshless methodsPDEs