Strong Stability Preserving General Linear Methods

We investigate the strong stability preserving (SSP) general linear methods with two and three external stages and s internal stages. We also describe the construction of starting procedures for these methods. Examples of SSP methods are derived of order p=2,p=3, and p=4 with 2≤s≤10 stages, which have larger effective Courant–Friedrichs–Levy coefficients than the class of two-step Runge–Kutta methods introduced by Jackiewicz and Tracogna, whose SSP properties were analyzes recently by Ketcheson, Gottlieb, and MacDonald, and the class of multistep multistage methods investigated by Constantinescu and Sandu. Numerical examples illustrate that the class of methods derived in this paper achieve the expected order of accuracy and do not produce spurious oscillations for discretizations of hyperbolic conservation laws, when combined with appropriate discretizations in spatial variables.