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

Patrick Joly (1) , Jerónimo Rodríguez (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

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.

Patrick Joly, Jerónimo Rodríguez. Optimized higher order time discretization of second order hyperbolic problems: Construction and numerical study. Journal of Computational and Applied Mathematics, 2009, 234 (6), pp.1953-1961. ⟨10.1016/j.cam.2009.08.046⟩. ⟨hal-00976330⟩