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Strong Stability Preserving General Linear Methods with Runge–Kutta Stability

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Abstract

We investigate strong stability preserving (SSP) general linear methods (GLMs) for systems of ordinary differential equations. Such methods are obtained by the solution of the minimization problems with nonlinear inequality constrains, corresponding to the SSP property of these methods, and equality constrains, corresponding to order and stage order conditions. These minimization problems were solved by the sequential quadratic programming algorithm implemented in MATLAB\(^{\circledR }\) subroutine fmincon.m starting with many random guesses. Examples of transformed SSP GLMs of order \(p = 1, 2, 3\), and 4, and stage order \(q = p\) have been determined, and suitable starting and finishing procedures have been constructed. The numerical experiments performed on a set of test problems have shown that transformed SSP GLMs constructed in this paper are more accurate than transformed SSP DIMSIMs and SSP Runge–Kutta methods of the same order.

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Acknowledgements

The research reported in this paper was started during the visit of the first author (GC) to Arizona State University in the Spring semester of 2017. This author wish to express her gratitude to the School of Mathematical and Statistical Sciences for hospitality during this visit. We would also like to express our gratitude to anonymous referees whose comments helped us to improve the presentation of this paper.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Salerno, Fisciano, SA, Italy

    Giovanna Califano

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

    Giuseppe Izzo

  3. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

    Zdzisław Jackiewicz

  4. Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

    Zdzisław Jackiewicz

Authors
  1. Giovanna Califano
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  2. Giuseppe Izzo
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  3. Zdzisław Jackiewicz
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Corresponding author

Correspondence to Giuseppe Izzo.

Additional information

Giovanna Califano: The work of this author was supported by an UNISA research Grant. Giuseppe Izzo: The work of this author was partially supported by GNCS-INdAM.

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Califano, G., Izzo, G. & Jackiewicz, Z. Strong Stability Preserving General Linear Methods with Runge–Kutta Stability. J Sci Comput 76, 943–968 (2018). https://doi.org/10.1007/s10915-018-0646-5

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  • DOI: https://doi.org/10.1007/s10915-018-0646-5

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