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Cao, C.S., Holm, D.D. and Titi, E.S. (2004) Traveling Wave Solutions for a Class of One-Dimensional Nonlinear Shallow Water Wave Models. Journal of Dynamics and Differential Equations, 16, 167-178.

has been cited by the following article:

• TITLE: On the Conservative Finite Difference Scheme for the Generalized Novikov Equation

  AUTHORS: Wenxia Chen, Qianqian Zhu, Ping Yang

  KEYWORDS: Generalized Novikov Equation, Finite Difference Scheme, Conservation Law, Stability, Convergence

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.9, September 22, 2017

  ABSTRACT: In this paper, we investigate a numerical method for the generalized Novikov equation. We propose a conservative finite difference scheme and use Brouwer fixed point theorem to obtain the existence of the solution of the corresponding difference equation. We also prove the convergence and stability of the solution by using the discrete energy method. Moreover, we obtain the truncation error of the difference scheme which is .