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On the linear stability of the fifth-order WENO discretization

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...

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M. Motamed More by this author
C. B. Macdonald More by this author
S. J. Ruuth More by this author
Publication date:
2010
URN:
uuid:b48a4adc-815d-439a-8012-2d7ac5053a28
Local pid:
oai:eprints.maths.ox.ac.uk:1011

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