Optimized higher order time discretization of second order hyperbolic problems: Construction and numerical study

Authors:
P. Joly;J. Rodríguez
Affiliations:
Team-Project Poems, UMR 2706 CNRS-INRIA-ENSTA, INRIA Rocquencourt, BP105, Le Chesnay, France;Team-Project Poems, UMR 2706 CNRS-INRIA-ENSTA, INRIA Rocquencourt, BP105, Le Chesnay, France and Departamento de Matemática Aplicada, USC, 15782 Santiago de Compostela, A Coruña, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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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. The optimal schemes are validated through various numerical results.