Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations

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• 作者：Wansheng Wang ^{w.s.wang@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Neutral delay differential equations ; Long-time behaviour ; Uniform ultimate boundedness ; Runge&ndash ; Kutta methods
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：132-144
• 全文大小：1278 K

文摘

This paper is concerned with the long-time behaviour of the numerical solutions generated by Runge–Kutta (RK) methods for nonlinear neutral delay differential equations (NDDEs). It is proved that the numerical solutions produced by (k,l$k,l$)-algebraically stable RK methods are uniformly ultimately bounded. Some examples reveal that some RK methods completely preserve the long-time behaviour of the exact solutions to NDDEs for sufficiently small time stepsize h$h$. As a comparison with the previous results, a numerical example which further illustrates our theoretical results is provided.