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oai:riuma.uma.es:10630/265702026-02-03T10:58:23Zcom_10630_2254col_10630_37953

Padé numerical schemes with Richardson extrapolation for the sine–Gordon equation Martín-Vergara, Francisca Rus-Mansilla, Francisco de Asís Villatoro-Machuca, Francisco Román Ecuaciones diferenciales Métodos numéricos Versión preprint ya que por motivos de derechos de propiedad intelectual no es posible subir la versión publicada del artículo. Four novel implicit finite difference methods with ( q + s ) -th order in space based on ( q, s )-Padé approximations have been analyzed and developed for the sine-Gordon equation. Specifically, (4,0)-, (2,2)-, (4,2)-, and (4,4)-Padé methods. All of them share the treatment for the nonlinearity and integration in time, specifically, the one that results in an energy-conserving (2,0)-Padé scheme. The five methods have been developed with and without Richardson extrapolation in time. All the methods are linearly, unconditionally stable. A comparison among them for both the kink–antikink and breather solutions in terms of global error, computational cost and energy conservation is presented. Our results indicate that the (4,0)- and (4,4)-Padé methods without Richardson extrapolation are the most cost-effective ones for small and large global error, respectively; and the (4,4)-Padé methods in all the cases when Richardson extrapolation is used. 2023-05-16T09:17:31Z 2023-05-16T09:17:31Z 2020 journal article F. Martin-Vergara, F. Rus, F.R. Villatoro. ”Padé schemes with Richardson’s extrapolation for the sine–Gordon equation,” Communications in Nonlinear Science and Numerical Simulation 85: 105243 (2020). ISSN 1007-5704, doi:10.1016/j.cnsns.2020.105243. 1007-5704 https://hdl.handle.net/10630/26570 10.1016/j.cnsns.2020.105243 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier