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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:309

Article

Wang, Wansheng¹ 

[1] Changsha Univ Sci & Technol, Sch Math & Computat Sci, Changsha 410114, Hunan, Peoples R China

关键词: Neutral delay differential equations;    Long-time behaviour;    Uniform ultimate boundedness;    Runge-Kutta methods;   

DOI  :  10.1016/j.cam.2016.06.027

来源: Elsevier

【 摘 要 】

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)-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. As a comparison with the previous results, a numerical example which further illustrates our theoretical results is provided. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free