RT Journal Article
T1 Padé numerical schemes for the sine–Gordon equation
A1 Martín-Vergara, Francisca
A1 Villatoro-Machuca, Francisco Román
A1 Rus Mansilla, Francisco
K1 Ondas electromagnéticas -- Propagación
K1 Solitones
K1 Métodos numéricos
AB 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.
PB Elsevier
YR 2019
FD 2019
LK https://hdl.handle.net/10630/26569
UL https://hdl.handle.net/10630/26569
LA eng
NO 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.
NO Versión preprint ya que por motivos de derechos de propiedad intelectual no es posible subir la versión publicada del artículo.
NO Projects EphemeCH (TIN2014-56494-C4-1-P) and DeepBIO (TIN2017-85727-C4-1-P) of the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia del Ministerio de Ciencia e Innovación of Spain.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026