Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 30, Issue 4, Pages 2113-2136Publisher
SIAM PUBLICATIONS
DOI: 10.1137/07070485X
Keywords
method of lines; strong stability-preserving; monotonicity; low-storage; Runge-Kutta methods
Categories
Ask authors/readers for more resources
Strong stability-preserving (SSP) Runge-Kutta methods were developed for time integration of semidiscretizations of partial differential equations. SSP methods preserve stability properties satisfied by forward Euler time integration, under a modified time-step restriction. We consider the problem of finding explicit Runge-Kutta methods with optimal SSP time-step restrictions, first for the case of linear autonomous ordinary differential equations and then for nonlinear or nonautonomous equations. By using alternate formulations of the associated optimization problems and introducing a new, more general class of low-storage implementations of Runge-Kutta methods, new optimal low-storage methods and new low-storage implementations of known optimal methods are found. The results include families of low-storage second and third order methods that achieve the maximum theoretically achievable effective SSP coefficient (independent of stage number), as well as low-storage fourth order methods that are more efficient than current full-storage methods. The theoretical properties of these methods are confirmed by numerical experiment.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available