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oai:gredos.usal.es:10366/1553372026-01-13T15:58:37Zcom_10366_4137com_10366_4055com_10366_3946com_10366_3823col_10366_4138

Martín Vaquero, Jesús Hernández Encinas, María Ascensión Queiruga Dios, María Araceli Gayoso Martínez, Víctor Martín del Rey, Ángel María 2024-02-05T12:07:50Z 2024-02-05T12:07:50Z 2018 Martín-Vaquero, J. (2018) “Numerical schemes for general Klein–Gordon equations with Dirichlet and nonlocal boundary conditions”, Nonlinear Analysis: Modelling and Control, 23(1), pp. 50–62. doi:10.15388/NA.2018.1.5. 1392-5113 http://hdl.handle.net/10366/155337 10.15388/NA.2018.1.5 [EN]In this work, we address the problem of solving nonlinear general Klein–Gordonequations (nlKGEs). Different fourth- and sixth-order, stable explicit and implicit, finite differenceschemes are derived. These new methods can be considered to approximate all type of Klein–Gordon equations (KGEs) including phi-four, forms I, II, and III, sine-Gordon, Liouville, dampedKlein–Gordon equations, and many others. These KGEs have a great importance in engineeringand theoretical physics.The higher-order methods proposed in this study allow a reduction in the number of nodes, whichmight also be very interesting when solving multi-dimensional KGEs. We have studied the stabilityand consistency of the proposed schemes when considering certain smoothness conditions of thesolutions. Additionally, both the typical Dirichlet and some nonlocal integral boundary conditionshave been studied. Finally, some numerical results are provided to support the theoretical aspectspreviously considered eng Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Klein–Gordon equations nonlocal boundary conditions finite difference methods consistency stability Numerical schemes for general Klein–Gordon equations with Dirichlet and nonlocal boundary conditions info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://doi.org/10.15388/NA.2018.1.5 Nonlinear Analysis: Modelling and Control 23 1 50 62