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2014•SIAM Journal on Numerical AnalysisRequires access

Asymptotic Stability of Linear Neutral Delay Differential-Algebraic Equations and Runge--Kutta Methods

Hongjiong Tian, Quanhong Yu, Jiaoxun Kuang

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Abstract

This paper is concerned with asymptotic stability of linear neutral delay differential-algebraic equations and Runge--Kutta methods. First, we give a new equivalent sufficient condition for the neutral delay differential-algebraic equations to be delay-independent asymptotically stable. Then we investigate the asymptotic stability of the numerical solutions generated by the Runge--Kutta methods combined with Lagrange interpolation. Some results on the asymptotic stability of Runge--Kutta methods of high order are given. Finally, numerical examples of index 1 and 2 are conducted to confirm our numerical stability result.

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What this paper is about

This paper is concerned with asymptotic stability of linear neutral delay differential-algebraic equations and Runge--Kutta methods. First, we give a new equivalent sufficient condition for the neutral delay differential-algebraic equations to be delay-independent asymptotically stable. Then we investigate the asymptotic stability of the numerical solutions generated by the Runge--Kutta methods combined with Lagrange interpolation. Some results on the asymptotic stability of Runge--Kutta methods of high order are given. Finally, numerical examples of index 1 and 2 are conducted to confirm our numerical stability result.

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OpenAlex reports 19 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper is concerned with asymptotic stability of linear neutral delay differential-algebraic equations and Runge--Kutta methods. First, we give a new equivalent sufficient condition for the neutral delay differential-algebraic equations to be delay-independent asymptotically stable. Then we investigate the asymptotic stability of the numerical solutions generated by the Runge--Kutta methods combined with Lagrange interpolation. Some results on the asymptotic stability of Runge--Kutta methods of high order are given. Finally, numerical examples of index 1 and 2 are conducted to confirm our numerical stability result.

Key concepts: Mathematics, Runge–Kutta methods, Delay differential equation, Exponential stability, Algebraic number, Stability (learning theory), Numerical stability, Interpolation (computer graphics)

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