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 ...

We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions stochastic driven by processes that are rougher than a Brownian motion. use Taylor series representation (B-series) both the numerical scheme and solution of equation in order determine conditions guarantee desired local error underlying method. Subsequently, we prove global given rate. In add...