Strong stability preserving explicit Runge-Kutta methods of maximal effective order (Q2855102)

The authors use the theory of strong stability preserving (SSP) time discretizations with Butcher's algebraic interpretation of order to construct explicit SSP Runge-Kutta schemes with an effective order of accuracy. These methods, when accompanied by starting and stopping methods, attain an order of accuracy higher than their (classical) order. The authors propose a new choice of starting and stopping methods to allow the overall procedure to be SSP. Moreover, they prove that explicit Runge-Kutta methods with strictly positive weights have at most effective order four. Numerical experiments demonstrate the validity of these methods in practice.