Geodesic
Delay-dependent stability of linear multi-step methods for linear neutral systems
Kybernetika, Tome 56 (2020) no. 3, pp. 543-558.

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In this paper, we are concerned with numerical methods for linear neutral systems with multiple delays. For delay-dependently stable neutral systems, we ask what conditions must be imposed on linear multi-step methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. Combining with Lagrange interpolation, linear multi-step methods can be applied to the neutral systems. Utilizing the argument principle, a sufficient condition is derived for linear multi-step methods with preserving delay-dependent stability. Numerical examples are given to illustrate the main results.
DOI : 10.14736/kyb-2020-3-0543
Classification : 65L05, 65L07, 65L20
Keywords: neutral systems with multiple delays; delay-dependent stability; linear multi-step method; Lagrange interpolation; argument principle 
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Hu, Guang-Da; Shao, Lizhen. Delay-dependent stability of linear multi-step methods for linear neutral systems. Kybernetika, Tome 56 (2020) no. 3, pp. 543-558. doi : 10.14736/kyb-2020-3-0543. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-3-0543/

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