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Delay-dependent stability of linear multistep methods for DAEs with multiple delays

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Abstract

This paper aims to investigate the asymptotic stability of linear multistep (LM) methods for linear differential-algebraic equations (DAEs) with multiple delays. Based on the argument principle, we first establish the delay-dependent stability criteria of analytic solutions; then, we propose some practically checkable conditions for weak delay-dependent stability of numerical solutions derived by implicit LM methods. Lagrange interpolations are used to compute the delayed terms. Several numerical examples are given to illustrate the theoretical results.

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Acknowledgements

The authors would like to thank the reviewers very much for their careful reviews and valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Xiulin Hu, Yuhao Cong & Guang-Da Hu

  2. Department of Mathematics and Physics, Hefei University, Hefei, 230601, China

    Xiulin Hu

Authors
  1. Xiulin Hu
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  2. Yuhao Cong
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  3. Guang-Da Hu
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Corresponding author

Correspondence to Guang-Da Hu.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11371053 and No. 11471217), Visting Scholar Key Program of Anhui Province (No. gxfxZD2016215), Natural Science Research Project of Anhui Province (No. KJ2015A253) and Research Fund Project of Hefei University (No. 17ZR05ZDA).

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Hu, X., Cong, Y. & Hu, GD. Delay-dependent stability of linear multistep methods for DAEs with multiple delays. Numer Algor 79, 719–739 (2018). https://doi.org/10.1007/s11075-017-0457-z

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  • DOI: https://doi.org/10.1007/s11075-017-0457-z

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