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

Jean-Charles Gilbert and Patrick Joly

2008

Publication type:

Paper in peer-reviewed journals

Journal:

Partial Differential Equations : Modeling and Numerical Simulation, vol. 16, pp. 67--93

Publisher:

Springer

DOI:

10.1007/978-1-4020-8758-5_4

HAL:

hal-00976773

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.

BibTeX:

@article{Gil-Jol-2008,
    author={Jean-Charles Gilbert and Patrick Joly },
    title={Higher order time stepping for second order hyperbolic 
           problems and optimal CFL conditions },
    doi={10.1007/978-1-4020-8758-5_4 },
    journal={Partial Differential Equations : Modeling and Numerical 
           Simulation },
    year={2008 },
    volume={16 },
    pages={67--93},
}