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    On the Linear Stability of the Fifth-Order WENO Discretization

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    Type
    Article
    Authors
    Motamed, Mohammad
    Macdonald, Colin B.
    Ruuth, Steven J.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2010-10-03
    Online Publication Date
    2010-10-03
    Print Publication Date
    2011-05
    Permanent link to this record
    http://hdl.handle.net/10754/599059
    
    Metadata
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    Abstract
    We 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.
    Citation
    Motamed 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.
    Sponsors
    The 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.
    Publisher
    Springer Nature
    Journal
    Journal of Scientific Computing
    DOI
    10.1007/s10915-010-9423-9
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10915-010-9423-9
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