Existence of the discrete travelling waves for a relaxing scheme

Hailiang Liu Jinghua Wang Tong Yang

Analysis of PDEs mathscidoc:1912.43993

Applied Mathematics Letters, 10, (3), 117-122, 1997.5
The existence of a discrete travelling wave is proved for the relaxing scheme. The main idea is to change the original scheme such that the resulting scheme is monotonic to which Jennings' result can be applied. The equivalence of the resulting scheme and the original one is shown when = 1 q. The u-component of the discrete travelling wave thus obtained is a discrete shock for a monotone conservative difference scheme, which approximates the corresponding conservation law.
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@inproceedings{hailiang1997existence,
  title={Existence of the discrete travelling waves for a relaxing scheme},
  author={Hailiang Liu, Jinghua Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211116711883557},
  booktitle={Applied Mathematics Letters},
  volume={10},
  number={3},
  pages={117-122},
  year={1997},
}
Hailiang Liu, Jinghua Wang, and Tong Yang. Existence of the discrete travelling waves for a relaxing scheme. 1997. Vol. 10. In Applied Mathematics Letters. pp.117-122. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211116711883557.
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