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01-09-2021 | Issue 3/2021

Calcolo 3/2021

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

Calcolo > Issue 3/2021
Meijun Wu, Quanhong Yu, Jiaoxun Kuang, Hongjiong Tian
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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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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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