Title : Higher order time stepping for second order hyperbolic problems and optimal CFL conditions
Year : 2008
Type : paper in peer-reviewed journal
Authors : J.-C. Gilbert, P. Joly
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.
Themes :
Reference : Partial Differential Equations : Modeling and Numerical Simulation - Springer - vol. 16 (pp 67--93 )