Optimal Explicit Strong-Stability-Preserving General Linear Methods

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. Key words. general linear methods, method of lines, strong-stability-preserving, monotonicity AMS subject classifications. 65M20, 65L06

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Emil M. Constantinescu, Adrian Sandu
• Keywords: General Linear, General Linear Methods, Linear Time-stepping Methods, SIAMSC 2010