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Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions

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Partial Differential Equations

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 16))

Summary

We investigate explicit higher order time discretizations of linear second order hyperbolic problems. We study the even order (2m) schemes obtained by the modified equation method. We show that the corresponding CFL upper bound for the time step remains bounded when the order of the scheme increases. We propose variants of these schemes constructed to optimize the CFL condition. The corresponding optimization problem is analyzed in detail and the analysis results in a specific numerical algorithm. The corresponding results are quite promising and suggest various conjectures.

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Author information

Authors and Affiliations

  1. INRIA Rocquencourt, BP 105, 78153, Le Chesnay, France

    J. Charles Gilbert & Patrick Joly

Authors
  1. J. Charles Gilbert
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  2. Patrick Joly
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Houston, USA

    Roland Glowinski

  2. Department of Mathematical Information Technology, University of Jyväskylä, Finland

    Pekka Neittaanmäki

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Gilbert, J.C., Joly, P. (2008). Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions. In: Glowinski, R., Neittaanmäki, P. (eds) Partial Differential Equations. Computational Methods in Applied Sciences, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8758-5_4

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