LANS Publications

"Optimal Explicit Strong-Stability-Preserving General Linear Methods"

E. M. Constantinescu and A. Sandu

SIAM J. Sci. Comput., vol. 32, , pp. 3130-3150. Also Preprint ANL/MCS-P1584-0209

Preprint Version: [pdf]

This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both
Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A global optimization strategy is used to find the most efficient schemes that have low storage requirements. Numerical results illustrate the theoretical findings.