Strong Stability Preserving Runge–Kutta and Linear Multistep Methods

Abstract This paper reviews strong stability preserving discrete variable methods for differential systems. The Runge–Kutta have been usually investigated in the literature on subject, using so-called Shu–Osher representation of these methods, as a convex combination first-order steps by forward Euler method. In this paper, we revisit analysis reformulating subclass general linear ordinary equations, and then characterization monotone which was derived Spijker his seminal (SIAM J Numer Anal 45:1226–1245, 2007). Using new approach, explicit implicit up to order four are derived. These equivalent RK obtained or generalized representation. We also investigate multistep again monotonicity theory Spijker.