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M. A. Lynch, “Large Amplitude Instability in Finite Difference Approximates to the Klein-Gordon Equation,” Applied Numerical Mathematics, Vol. 31, No. 2, 1999, pp. 173-182. doi:10.1016/S0168-9274(98)00128-7

has been cited by the following article:

• TITLE: Numerical Solution of Nonlinear Klein-Gordon Equation Using Lattice Boltzmann Method

  AUTHORS: Qiaojie Li, Zong Ji, Zhoushun Zheng, Hongjuan Liu

  KEYWORDS: Lattice Boltzmann, Chapman-Enskog Expansion, Nonlinear Klein-Gordon Equation

  JOURNAL NAME: Applied Mathematics, Vol.2 No.12, December 27, 2011

  ABSTRACT: In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a one-dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on some test examples, and the numerical results have been compared with the analytical solutions or the numerical solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show the efficiency of the method computationally.