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dc.contributor.authorRanocha, Hendrik
dc.contributor.authorMitsotakis, Dimitrios
dc.contributor.authorKetcheson, David I.
dc.date.accessioned2020-12-01T13:20:22Z
dc.date.available2020-12-01T13:20:22Z
dc.date.issued2020-06-26
dc.identifier.urihttp://hdl.handle.net/10754/666203.1
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.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2006.14802
dc.rightsArchived with thanks to arXiv
dc.titleA Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.eprint.versionPre-print
dc.contributor.institutionSchool of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand.
dc.identifier.arxivid2006.14802
kaust.personRanocha, Hendrik
kaust.personKetcheson, David I.
refterms.dateFOA2020-12-01T13:20:53Z


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