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.

%B SIAM J. Sci. Comput. %V 32 %P 3130-3150 %8 10/2010 %G eng %U http://epubs.siam.org/sisc/resource/1/sjoce3/v32/i5/p3130_s1 %N 5 %1 http://www.mcs.anl.gov/papers/P1584.pdf