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On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations

dc.contributor.authorRanocha, Hendrik
dc.contributor.authorQuezada de Luna, Manuel
dc.contributor.authorKetcheson, David I.
dc.date.accessioned2021-11-21T13:48:00Z
dc.date.available2021-11-21T13:48:00Z
dc.date.issued2021-10-18
dc.date.submitted2021-06-09
dc.identifier.citationRanocha, H., de Luna, M. Q., & Ketcheson, D. I. (2021). On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations. Partial Differential Equations and Applications, 2(6). doi:10.1007/s42985-021-00126-3
dc.identifier.issn2662-2963
dc.identifier.issn2662-2971
dc.identifier.doi10.1007/s42985-021-00126-3
dc.identifier.urihttp://hdl.handle.net/10754/673702
dc.description.abstractAbstractWe study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.
dc.description.sponsorshipOpen Access funding enabled and organized by Projekt DEAL.
dc.description.sponsorshipWe thank Prof. Ángel Durán for his insightful and very detailed comments on an early draft that helped us to improve this work, and for helping us learn the theory of relative equilibrium solutions. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure.
dc.publisherSpringer Science and Business Media LLC
dc.relation.urlhttps://link.springer.com/10.1007/s42985-021-00126-3
dc.rightsWe thank Prof. Ángel Durán for his insightful and very detailed comments on an early draft that helped us to improve this work, and for helping us learn the theory of relative equilibrium solutions. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.titleOn the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Mathematics Group
dc.identifier.journalPartial Differential Equations and Applications
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionApplied Mathematics Münster, University of Münster, Münster, Germany.
dc.identifier.volume2
dc.identifier.issue6
dc.identifier.arxivid2102.07376
kaust.personQuezada de Luna, Manuel
kaust.personKetcheson, David I.
dc.date.accepted2021-09-20
refterms.dateFOA2021-11-21T13:48:45Z
dc.date.published-online2021-10-18
dc.date.published-print2021-12
dc.date.posted2021-02-15


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We thank Prof. Ángel Durán for his insightful and very detailed comments on an early draft that helped us to improve this work, and for helping us learn the theory of relative equilibrium solutions. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure.
Except where otherwise noted, this item's license is described as We thank Prof. Ángel Durán for his insightful and very detailed comments on an early draft that helped us to improve this work, and for helping us learn the theory of relative equilibrium solutions. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure.