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Fully discrete spectral methods for solving time fractional nonlinear Sine–Gordon equation with smooth and non-smooth solutions

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  • Liu, Zeting
  • Lü, Shujuan
  • Liu, Fawang

Abstract

We consider the initial boundary value problem of the time fractional nonlinear Sine–Gordon equation and the fractional derivative is described in Caputo sense with the order α(1 < α < 2). Two fully discrete schemes are developed based on Legendre spectral approximation in space and finite difference discretization in time for smooth solutions and non-smooth solutions, respectively. Numerical stability and convergence are analysed. Numerical experiments for both the fully discrete schemes are presented to confirm our theoretical analysis.

Suggested Citation

  • Liu, Zeting & Lü, Shujuan & Liu, Fawang, 2018. "Fully discrete spectral methods for solving time fractional nonlinear Sine–Gordon equation with smooth and non-smooth solutions," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 213-224.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:213-224
    DOI: 10.1016/j.amc.2018.03.069
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    References listed on IDEAS

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    1. Laskin, N. & Zaslavsky, G., 2006. "Nonlinear fractional dynamics on a lattice with long range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 38-54.
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    Cited by:

    1. Xu, Yibin & Liu, Yanqin & Yin, Xiuling & Feng, Libo & Wang, Zihua & Li, Qiuping, 2023. "A fast time stepping Legendre spectral method for solving fractional Cable equation with smooth and non-smooth solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 154-170.
    2. Li, Meng & Fei, Mingfa & Wang, Nan & Huang, Chengming, 2020. "A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 404-419.

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