Kybernetika 56 no. 3, 543-558, 2020

Delay-dependent stability of linear multi-step methods for linear neutral systems

Guang-Da Hu and Lizhen ShaoDOI: 10.14736/kyb-2020-3-0543

Abstract:

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.

Keywords:

delay-dependent stability, Lagrange interpolation, argument principle, neutral systems with multiple delays, linear multi-step method

Classification:

65L05, 65L07, 65L20

paper.pdf

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