Geodesic
Delay-dependent stability of Runge-Kutta methods for linear neutral systems with multiple delays
Kybernetika, Tome 54 (2018) no. 4, pp. 718-735.

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In this paper, we are concerned with stability of numerical methods for linear neutral systems with multiple delays. Delay-dependent stability of Runge-Kutta methods is investigated, i. e., for delay-dependently stable systems, we ask what conditions must be imposed on the Runge-Kutta methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. By means of Lagrange interpolation, Runge-Kutta methods can be applied to neutral differential systems with multiple delays. Based on the argument principle, sufficient conditions for delay-dependent stability of Runge-Kutta methods combined with Lagrange interpolation are presented. Numerical examples are given to illustrate the main results.
DOI : 10.14736/kyb-2018-4-0718
Classification : 65L05, 65L07, 65L20
Keywords: neutral differential systems with multiple delays; delay-dependent stability; Runge–Kutta method; Lagrange interpolation; argument principle 
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     title = {Delay-dependent stability of {Runge-Kutta} methods for linear neutral systems with multiple delays},
     journal = {Kybernetika},
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     volume = {54},
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     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-4-0718/}
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Hu, Guang-Da. Delay-dependent stability of Runge-Kutta methods for linear neutral systems with multiple delays. Kybernetika, Tome 54 (2018) no. 4, pp. 718-735. doi : 10.14736/kyb-2018-4-0718. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-4-0718/

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