Optimal Explicit Strong-Stability-Preserving General Linear Methods: Complete Results

TitleOptimal Explicit Strong-Stability-Preserving General Linear Methods: Complete Results
Publication TypeReport
Year of Publication2009
AuthorsConstantinescu, EM, Sandu, A
Report NumberANL/MCS-TM-304
AbstractThis 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.    
PDFhttp://www.mcs.anl.gov/papers/TM304A.pdf