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Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays

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This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Shanghai, 200234, People’s Republic of China

    Meijun Wu, Jiaoxun Kuang & Hongjiong Tian

  2. College of Information Technology, Shanghai Ocean University, 999 City Loop, Lingang New City, Shanghai, 201306, People’s Republic of China

    Quanhong Yu

  3. Scientific Computing Key Laboratory of Shanghai Universities, 100 Guilin Road, Shanghai, 200234, People’s Republic of China

    Hongjiong Tian

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  1. Meijun Wu
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  2. Quanhong Yu
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The work of this author is supported in part by the National Natural Science Foundation of China under Grant Nos. 11671266 and 11871343.

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Wu, M., Yu, Q., Kuang, J. et al. Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays. Calcolo 58, 37 (2021). https://doi.org/10.1007/s10092-021-00428-3

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  • DOI: https://doi.org/10.1007/s10092-021-00428-3

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