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Strong Stability Preserving Integrating Factor General Linear Methods

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Abstract

In this paper, we discuss the numerical solution of systems of differential equations with both linear (stiff) and nonlinear components that arise from the semi-discretization of certain partial differential equations. When faced with the task of solving problems with discontinuous solutions numerically, the linear stability properties are insufficient for convergence. So, to overcome this drawback, strong stability preserving (SSP) methods are introduced. While using SSP implicit-explicit methods lead to severe constraints on the allowed time-stepping, an integrating factor approach reduces this limitation by solving the linear part exactly. In this work, we develop integrating factor general linear methods (IFGLMs) with strong stability properties. Sufficient conditions for IFGLMs to be SSP are discussed. The construction of IFGLMs of order \(p\le 6\) and stage order \(1\le q\le p\) with \(r=p\) external stages and \(2\le s\le 10\) internal stages is presented, which have larger effective SSP coefficients than the class of Runge–Kutta and two–step Runge–Kutta methods. Results are verified numerically on several representative test cases.

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Authors and Affiliations

  1. Faculty of Science, University of Maragheh, Maragheh, Iran

    Pari Khakzad, Mohammad Mehdizadeh Khalsaraei & Ali Shokri

  2. Department of Information Engineering and Information Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Afsaneh Moradi

  3. Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Gholamreza Hojjati

  4. Research Department of Computational Algorithms and Mathematical Models, University of Tabriz, Tabriz, Iran

    Gholamreza Hojjati

Authors
  1. Pari Khakzad
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  2. Afsaneh Moradi
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  3. Gholamreza Hojjati
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  4. Mohammad Mehdizadeh Khalsaraei
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  5. Ali Shokri
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Correspondence to Gholamreza Hojjati or Mohammad Mehdizadeh Khalsaraei.

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Khakzad, P., Moradi, A., Hojjati, G. et al. Strong Stability Preserving Integrating Factor General Linear Methods. Comp. Appl. Math. 42, 214 (2023). https://doi.org/10.1007/s40314-023-02356-0

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  • DOI: https://doi.org/10.1007/s40314-023-02356-0

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