Tailoring High Order Time Discretizations for Use with Spatial Discretizations of Hyperbolic PDEs

Abstract : The major accomplishment of the current research was to overcome the time-stepping constraints and the order barriers on explicit and implicit strong stability preserving methods. This was attained through the study of multi-step multistage methods, multi-derivative methods, methods of variable linear and nonlinear orders, and methods which include downwinding. The results of this work include four families of new SSP methods which break order barriers and time-step bounds of previously known methods.