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Padé numerical schemes for the sine–Gordon equation Martín-Vergara, Francisca Villatoro-Machuca, Francisco Román Rus Mansilla, Francisco Ondas electromagnéticas -- Propagación Solitones Métodos numéricos Versión preprint ya que por motivos de derechos de propiedad intelectual no es posible subir la versión publicada del artículo. The sine-Gordon equation turn up in several problems in science and engineering. Although it is integrable, in practical applications, its numerical solution is powerful and versatile. Four novel implicit finite difference methods based on ( q , s ) Padé approximations with ( q + s ) th order in space have been developed and analyzed for this equation; all share the same treatment for the nonlinearity and integration in time. Concretely, (0,4), (2,2), (2,4), and (4,4) Padé methods; additionally, the energy conserving, Strauss–Vázquez scheme has been considered in a (0,2) Padé implementation. These methods have been compared among them for both the kink–antikink and breather solutions in terms of global error, computational cost and energy conservation. The (0,4) and (2,4) Padé methods are the most cost-effective ones for small and large global error, respectively. Our results indicate that spatial order of accuracy is more relevant to effectiveness of a method than energy conservation even in very long time integrations. 2023-05-16T09:15:23Z 2023-05-16T09:15:23Z 2019 journal article F. Martin-Vergara, F. Rus, F.R. Villatoro, ”Padé numerical schemes for the sine–Gordon equation,” Applied Mathematics and Computation 358: 232–243 (2019). ISSN 0096-3003, doi:10.1016/j.amc.2019.04.042. https://hdl.handle.net/10630/26569 10.1016/j.amc.2019.04.042 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier