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Strong stability preserving implicit–explicit transformed general linear methods

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  • Izzo, Giuseppe
  • Jackiewicz, Zdzislaw

Abstract

We consider the class of implicit–explicit (IMEX) general linear methods (GLMs) to construct methods where the explicit part has strong stability preserving (SSP) property, while the implicit part of the method has inherent Runge–Kutta stability (IRKS) property, and it is A-, or L-stable. We will also investigate the absolute stability of these methods when the implicit and explicit parts interact with each other. In particular, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A(α)-stable for α∈[0,π∕2]. Finally we furnish examples of SSP IMEX GLMs up to the order p=4 and stage order q=p with optimal SSP coefficients.

Suggested Citation

  • Izzo, Giuseppe & Jackiewicz, Zdzislaw, 2020. "Strong stability preserving implicit–explicit transformed general linear methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 206-225.
    • Handle: RePEc:eee:matcom:v:176:y:2020:i:c:p:206-225
    DOI: 10.1016/j.matcom.2019.11.008
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    Cited by:

    1. Tan, Zengqiang & Zhang, Chengjian, 2022. "Numerical approximation to semi-linear stiff neutral equations via implicit–explicit general linear methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 68-87.

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