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The Properties of Multistep Runge-Kutta Methods for Neutral Delay Differential Equations

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Software Engineering and Algorithms (CSOC 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 230))

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Abstract

This paper is devoted to the stability and convergence analysis of the multistep Runge-Kutta methods with the Lagrange interpolation of the numerical solution for a nonlinear neutral delay differential equations. Nonlinear stability and D-Convergence 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 RK methods, we also discuss the D-convergence properties of multistep RK methods with a restricted type of interpolation procedure.

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Acknowledgements

The authors would like to thank the referees for giving helpful comments and suggestions. This research is supported by National Natural Science Foundation of China (Project No.11901173) and by the Heilongjiang province Natural Science Foundation (LH2019A030) and by the Innovation Talent Foundation of Heilongjiang institute of technology (2018CX17).

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Authors and Affiliations

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

    Kewei Zhang & Haiyan Yuan

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  1. Kewei Zhang
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  2. Haiyan Yuan
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Editors and Affiliations

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

    Radek Silhavy

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Zhang, K., Yuan, H. (2021). The Properties of Multistep Runge-Kutta Methods for Neutral Delay Differential Equations. In: Silhavy, R. (eds) Software Engineering and Algorithms. CSOC 2021. Lecture Notes in Networks and Systems, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-030-77442-4_57

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