Strong Stability Preserving Multistage Integration Methods

* The work of the first author (GI) was partially supported by GNCS-INdAM.

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

AMS Subject Classification:

• 65L06
• 65L20
• 65L99

Notes

* The work of the first author (GI) was partially supported by GNCS-INdAM.