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Stability and Dissipativity of Multistep Runge–Kutta Methods for Nonlinear Delay Differential Equations with Constrained Grid

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Computational Statistics and Mathematical Modeling Methods in Intelligent Systems (CoMeSySo 2019 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1047))

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Abstract

This paper is devoted to the stability and dissipativity of multistep Runge–Kutta methods with constrained grid for a class of nonlinear neutral delay differential equations. Nonlinear stability and dissipativity are introduced and proved. We discuss both the \( GR(l) \)-stability, \( GAR(l) \)-stability, and the weak \( GAR(l) \)-stability on the basis of \( (k,l) \)-algebraically stable of the multistep Runge–Kutta methods, we also prove that an algebraically stable, irreducible multistep Runge–Kutta method is finite-dimensional dissipative.

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Acknowledgments

This work was supported by Natural Science Foundation of China under Grant 11901173 and Heilongjiang Natural Science Foundation (LH2019A030) and the assisted project by Heilong Jiang Postdoctoral Funds for scientific research initiation and the Research Foundation of Heilongjiang Educational Committee (12531546).

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The authors declare that there is no conflict of interests regarding the publication of this article.

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Authors and Affiliations

  1. Department of Mathematics, Heilongjiang Institute of Technology, Harbin, 150050, China

    Yuhuan Fan, Haiyan Yuan & Peichen Wang

Authors
  1. Yuhuan Fan
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  2. Haiyan Yuan
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  3. Peichen Wang
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Corresponding author

Correspondence to Haiyan Yuan .

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Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlin, Zlin, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlin, Zlin, Czech Republic

    Petr Silhavy

  3. Faculty of Applied Informatics, Tomas Bata University in Zlin, Zlin, Czech Republic

    Zdenka Prokopova

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Fan, Y., Yuan, H., Wang, P. (2019). Stability and Dissipativity of Multistep Runge–Kutta Methods for Nonlinear Delay Differential Equations with Constrained Grid. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Computational Statistics and Mathematical Modeling Methods in Intelligent Systems. CoMeSySo 2019 2019. Advances in Intelligent Systems and Computing, vol 1047. Springer, Cham. https://doi.org/10.1007/978-3-030-31362-3_23

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