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Strong Stability Preserving General Linear Methods

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Abstract

We investigate the strong stability preserving (SSP) general linear methods with two and three external stages and \(s\) internal stages. We also describe the construction of starting procedures for these methods. Examples of SSP methods are derived of order \(p=2, p=3\), and \(p=4\) with \(2\le s\le 10\) stages, which have larger effective Courant–Friedrichs–Levy coefficients than the class of two-step Runge–Kutta methods introduced by Jackiewicz and Tracogna, whose SSP properties were analyzes recently by Ketcheson, Gottlieb, and MacDonald, and the class of multistep multistage methods investigated by Constantinescu and Sandu. Numerical examples illustrate that the class of methods derived in this paper achieve the expected order of accuracy and do not produce spurious oscillations for discretizations of hyperbolic conservation laws, when combined with appropriate discretizations in spatial variables.

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Acknowledgments

The results reported in this paper were obtained during the visit of the first author (GI) to the Arizona State University in the Spring semester of 2014. This author wish to express his gratitude to the School of Mathematical and Statistical Sciences for hospitality during this visit. The authors would also like to express their gratitude to anonymous referees for their useful comments which helped to improve presentation of this paper.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Napoli-“Federico II”, 80126, Napoli, Italy

    Giuseppe Izzo

  2. Department of Mathematics, Arizona State University, Tempe, AZ, 85287, USA

    Zdzislaw Jackiewicz

  3. AGH University of Science and Technology, Kraków, Poland

    Zdzislaw Jackiewicz

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  1. Giuseppe Izzo
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  2. Zdzislaw Jackiewicz
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Correspondence to Giuseppe Izzo.

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The work of the first author was partially supported by GNCS-INdAM.

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Izzo, G., Jackiewicz, Z. Strong Stability Preserving General Linear Methods. J Sci Comput 65, 271–298 (2015). https://doi.org/10.1007/s10915-014-9961-7

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