On Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations
(Sigal Gottlieb, University of Massachusetts, Dartmouth)

Strong stability preserving (SSP) high order time discretizations were
developed for the time evolution of hyperbolic partial differential equations
with discontinuous solutions.  Significant effort is expended in creating
spatial discretizations which satisfy certain nonlinear stability properties,
or non-oscillatory properties, usually when coupled with forward Euler.
Higher order SSP methods extend this by giving you a guarantee of provable
strong stability in any norm, semi-norm or convex functional, as long as the
spatial discretization had this property for forward Euler, under some
time-step restriction.  In this talk, I will present SSP multistep and
Runge-Kutta methods, both implicit and explicit, with optimal time-step
restrictions.