Efficient SSP low-storage Runge–Kutta methods

In this paper we study the efficiency of Strong Stability Preserving (SSP) Runge–Kutta methods that can be implemented with a low number registers using their Shu–Osher representation. SSP have been studied in literature and stepsize restrictions ensure numerical monotonicity found. However, for some problems, observed are larger than theoretical ones. Aiming at obtaining additional properties schemes may explain efficiency, influence local error term restrictions. For purpose, consider family 5-stage third order explicit methods, namely SSP(5,3), Buckley–Leverett equation. We deal optimal SSP(5,3) whose implementation requires least 3 memory registers, non-optimal 2-register schemes. The experiments done show small constants improve method sense coefficients obtained.