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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 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 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