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dc.contributor.authorRanocha, Hendrik
dc.contributor.authorMitsotakis, Dimitrios
dc.contributor.authorKetcheson, David I.
dc.date.accessioned2021-03-24T08:32:34Z
dc.date.available2020-12-01T13:20:22Z
dc.date.available2021-03-24T08:32:34Z
dc.date.issued2021-06
dc.date.submitted2020-06-26
dc.identifier.citationRanocha, H. (2021). A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations. Communications in Computational Physics, 29(4), 979–1029. doi:10.4208/cicp.oa-2020-0119
dc.identifier.issn1991-7120
dc.identifier.issn1815-2406
dc.identifier.doi10.4208/CICP.OA-2020-0119
dc.identifier.urihttp://hdl.handle.net/10754/666203
dc.description.abstractWe develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes of fully-discrete conservative methods for several nonlinear dispersive wave equations: Benjamin-Bona-Mahony (BBM), Fornberg-Whitham, Camassa-Holm, Degasperis-Procesi, Holm-Hone, and the BBM-BBM system. These full discretizations conserve all linear invariants and one nonlinear invariant for each system. The spatial semidiscretizations include finite difference, spectral collocation, and both discontinuous and continuous finite element methods. The time discretization is essentially explicit, using relaxation Runge-Kutta methods. We implement some specific schemes from among the derived classes, and demonstrate their favorable properties through numerical tests.
dc.publisherGlobal Science Press
dc.relation.urlhttp://global-sci.org/intro/article_detail/cicp/18643.html
dc.rightsArchived with thanks to Communications in Computational Physics
dc.titleA broad class of conservative numerical methods for dispersive wave equations
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalCommunications in Computational Physics
dc.eprint.versionPost-print
dc.contributor.institutionSchool of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand.
dc.identifier.volume29
dc.identifier.issue4
dc.identifier.pages979-1029
dc.identifier.arxivid2006.14802
kaust.personRanocha, Hendrik
kaust.personKetcheson, David I.
dc.date.accepted2020-11-10
dc.identifier.eid2-s2.0-85102641162
refterms.dateFOA2020-12-01T13:20:53Z
dc.date.published-online2021-06
dc.date.published-print2021-06
dc.date.posted2020-06-26


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