期刊论文

Wang, Wansheng

英文

Journal of Computational and Applied Mathematics

0377-0427

2017

309

C

132-144

10.1016/j.cam.2016.06.027

This work was supported by the Natural Science Foundation of China (Grant No. 11371074 ) and the Hunan Provincial Natural Science Foundation of China (Grant No. 13JJ1020 ), the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 13A108 ), and the Open Fund Project of Key Research Institute of Philosophies and Social Sciences in Hunan Universities .

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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 i...