Strong Stability Preserving Multistage Integration Methods

Abstract

In this paper we systematically investigate explicit strong stability preserving (SSP) multistage integration methods, a subclass of general linear methods (GLMs), of order p and stage order q ≤ p. Characterization of this class of SSP GLMs is given and examples of SSP methods of order p ≤ 4 and stage order q = 1, 2, . . . , p are provided. Numerical tests are reported which confirm that the constructed methods achieve the expected order of accuracy and preserve monotonicity.

Keywords

• multistage integration methods
• general linear methods
• strong stability preserving
• monotonicity
• two-step Runge–Kutta methods