Abstract
We present some remarks about the CFL condition for explicit time discretization methods of Adams–Bashforth and Runge–Kutta type and show that for convection-dominated problems stability conditions of the type Δt≤CΔx α are found for high order space discretizations, where the exponent α depends on the order of the time scheme. For example, for second order Adams–Bashforth and Runge–Kutta schemes we find α=4/3.
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Acknowledgements
K.S. is grateful to Carlos de Moura for the invitation to the conference “CFL-Condition, 80 years gone by”, held in Rio de Janeiro in May 2010.
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Schneider, K., Kolomenskiy, D., Deriaz, E. (2013). Is the CFL Condition Sufficient? Some Remarks. In: de Moura, C., Kubrusly, C. (eds) The Courant–Friedrichs–Lewy (CFL) Condition. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8394-8_9
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DOI: https://doi.org/10.1007/978-0-8176-8394-8_9
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