Higher order time stepping for second order hyperbolic problems and optimal CFL conditions

Jean-Charles Gilbert Patrick Joly 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : 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.
Type de document :
Chapitre d'ouvrage
Partial Differential Equations : Modeling and Numerical Simulation, 16, Springer, pp.67-93, 2008, 978-1-4020-8757-8. <10.1007/978-1-4020-8758-5_4>
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https://hal-ensta.archives-ouvertes.fr/hal-00976773
Contributeur : Aurélien Arnoux <>
Soumis le : jeudi 10 avril 2014 - 13:05:41
Dernière modification le : jeudi 9 février 2017 - 15:28:13

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Jean-Charles Gilbert, Patrick Joly. Higher order time stepping for second order hyperbolic problems and optimal CFL conditions. Partial Differential Equations : Modeling and Numerical Simulation, 16, Springer, pp.67-93, 2008, 978-1-4020-8757-8. <10.1007/978-1-4020-8758-5_4>. <hal-00976773>

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