Asymptotic stability of exact and discrete solutions for neutral multidelay-integro-differential equations

作者：Wang, Wansheng; Zhang, Chengjian^*; Li, Dongfang

来源：Applied Mathematical Modelling, 2011, 35(9): 4490-4506.

DOI：10.1016/j.apm.2011.03.019

• Neutral differential equations
• Delay-integro-differential equations
• Runge-Kutta methods
• Asymptotic stability

This paper concerns the long-time behavior of the exact and discrete solutions to a class of nonlinear neutral integro-differential equations with multiple delays. Using a generalized Halanay inequality, we give two sufficient conditions for the asymptotic stability of the exact solution to this class of equations. Runge-Kutta methods with compound quadrature rule are considered to discretize this class of equations with commensurate delays. Nonlinear stability conditions for the presented methods are derived. It is found that, under suitable conditions, this class of numerical methods retain the asymptotic stability of the underlying system. Some numerical examples that illustrate the theoretical results are given.

• 出版日期2011-9
• 单位长沙理工大学; 华中科技大学