Ureña, MiguelBenito Muñoz, Juan J.Ureña, FranciscoSalete Casino, EduardoGavete, LuisMuelas Rodríguez, Ángel2025-01-072025-01-072017-01-09Ureña, M., Benito, J., Ureña, F., Salete, E., Gavete, L. and Muelas, A. , (2019) Application of generalised finite differences method to reflection and transmission problems in seismic SH waves propagation. Mathematical Methods in the Applied Sciences, 41(6),Pages 2328-2339. https://doi.org/10.1002/mma.42680170-4214 e-ISSN: 1099-1476https://doi.org/10.1002/mma.4268https://hdl.handle.net/20.500.14468/25118La versión registrada de este artículo, publicado por primera vez en Mathematical Methods in the Applied Sciences, 41(6),Pages 2328-2339, está disponible en línea en el sitio web del editor: https://doi.org/10.1002/mma.4268 The copyrighted version of this article, first published in Mathematical Methods in the Applied Sciences, 41(6),Pages 2328-2339, is available online at the publisher's website: https://doi.org/10.1002/mma.4268A matrix formulation of the generalised finite difference method is introduced. A necessary and sufficient condition for the uniqueness of the solution is demonstrated, and important practical consequences are obtained. A generalised finite differences scheme for SH wave is obtained, the stability of the scheme is analysed and the formula for the velocity of the wave due to the scheme is obtained in order to deal with the numerical dispersion. The method is applied to seismic waves propagation problems, specifically to the problem of reflection and transmission of plane waves in heterogeneous media. A heterogeneous approach without nodes at the interface is chosen to solve the problem in heterogeneous media.eninfo:eu-repo/semantics/openAccess33 Ciencias Tecnológicas::3310 Tecnología industrialartículoMeshless methodsgeneralized finite difference methodgeophysics