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

Patrick Joly and Jerónimo Rodríguez

septembre, 2009

Publication type:

Paper in peer-reviewed journals

Journal:

Journal of Computational and Applied Mathematics, vol. 234(6), pp. 1953-1961

DOI:

10.1016/j.cam.2009.08.046

HAL:

hal-00976330

Keywords :

higher order discretization, CFL condition, time stepping, wave propagation problems, modified equation method

Abstract:

We investigate explicit higher order time discretizations of linear second order hyperbolic problems. We study the even order (2m2m) 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.

BibTeX:

@article{Jol-Rod-2009,
    author={Patrick Joly and Jerónimo Rodríguez },
    title={Optimized higher order time discretization of second order 
           hyperbolic problems: Construction and numerical study },
    doi={10.1016/j.cam.2009.08.046 },
    journal={Journal of Computational and Applied Mathematics },
    year={2009 },
    month={9},
    volume={234(6) },
    pages={1953--1961},
}