RT Journal Article
T1 Padé numerical schemes with Richardson extrapolation for the sine–Gordon equation
A1 Martín-Vergara, Francisca
A1 Rus-Mansilla, Francisco de Asís
A1 Villatoro-Machuca, Francisco Román
K1 Ecuaciones diferenciales
K1 Métodos numéricos
AB 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.
PB Elsevier
SN 1007-5704
YR 2020
FD 2020
LK https://hdl.handle.net/10630/26570
UL https://hdl.handle.net/10630/26570
LA eng
NO 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.
NO Versión preprint ya que por motivos de derechos de propiedad intelectual no es posible subir la versión publicada del artículo.
NO Project 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 SpainProject RoCoSoyCo (UMA18-FEDERJA-248) of the Consejería de Economía y Conocimiento, Junta de Andalucía, Spain.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026