Strong stability preserving transformed DIMSIMs

Abstract

In this paper we investigate the strong stability preserving (SSP) property of transformed diagonally implicit multistage integration methods (DIMSIMs). Within this class, examples of SSP methods of order p = 1 , 2 , 3 and 4 and stage order q = p have been determined, and also suitable starting and finishing procedure have been constructed. The numerical experiments performed on a set of test problems have shown that SSP transformed DIMSIMs can be more accurate and competitive with SSP Runge–Kutta methods of the same order.