Stability analysis of block boundary value methods for the neutral differential equation with many delays

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• 作者：Yang Xu ; Jingjun Zhao ; Zheng Gao
• 关键词：Neutral differential equation ; Block boundary value methods ; Asymptotic stability
• 刊名：Applied Mathematical Modelling
• 出版年：1 January, 2014
• 年：2014
• 卷：38
• 期：1
• 页码：325-335
• 全文大小：474 K

文摘

This paper mainly deals with the asymptotic stability properties of block boundary value methods (B₂VMs) for the neutral differential equation with many delays. For the time lagging arguments, a technique of Lagrange interpolation is considered. Under some certain conditions, it is proved that B₂VMs can preserve the asymptotic stability of exact solutions for the neutral differential equation with many delays if and only if B₂VMs are A-stable for ordinary differential equation. Moreover, some numerical experiments are given to confirm the main conclusion.