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dc.contributor.authorMotamed, Mohammad
dc.contributor.authorMacdonald, Colin B.
dc.contributor.authorRuuth, Steven J.
dc.date.accessioned2016-02-25T13:52:05Z
dc.date.available2016-02-25T13:52:05Z
dc.date.issued2010-10-03
dc.identifier.citationMotamed M, Macdonald CB, Ruuth SJ (2010) On the Linear Stability of the Fifth-Order WENO Discretization. Journal of Scientific Computing 47: 127–149. Available: http://dx.doi.org/10.1007/s10915-010-9423-9.
dc.identifier.issn0885-7474
dc.identifier.issn1573-7691
dc.identifier.doi10.1007/s10915-010-9423-9
dc.identifier.urihttp://hdl.handle.net/10754/599059
dc.description.abstractWe study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.
dc.description.sponsorshipThe work of M. Motamed was partially supported by NSERC Canada.The work of C. B. Macdonald was supported by NSERC Canada, NSF grant number CCF-0321917, and by Award No KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The work of S.J. Ruuth was partially supported by NSERC Canada.
dc.publisherSpringer Nature
dc.subjectHyperbolic conservation laws
dc.subjectLinear stability analysis
dc.subjectMethod of lines
dc.subjectMultistep methods
dc.subjectRunge-Kutta methods
dc.subjectWENO
dc.titleOn the Linear Stability of the Fifth-Order WENO Discretization
dc.typeArticle
dc.identifier.journalJournal of Scientific Computing
dc.contributor.institutionSimon Fraser University, Burnaby, Canada
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK-C1-013-04
dc.date.published-online2010-10-03
dc.date.published-print2011-05


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