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Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation

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  • Yan, Jingye
  • Zhang, Hong
  • Liu, Ziyuan
  • Song, Songhe

Abstract

We propose two conservative linear-implicit schemes for the space fractional Korteweg-de Vries (fKdV) equation. One is the linear-implicit Crank–Nicolson scheme and the other is the linear-implicit leap-frog scheme. In order to obtain a high order discretization in the space direction, we adopt the Fourier pseudospectral method. The Crank–Nicolson scheme and leap-frog scheme are used for temporal discretization, and those two schemes are efficient in practical computations because of their linear property. Furthermore, we analyse the uniqueness, boundness, convergence of the two schemes. Numerical experiments are presented to validate the theoretical analysis.

Suggested Citation

  • Yan, Jingye & Zhang, Hong & Liu, Ziyuan & Song, Songhe, 2020. "Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307374
    DOI: 10.1016/j.amc.2019.124745
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    References listed on IDEAS

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    1. Wang, Qi, 2008. "Homotopy perturbation method for fractional KdV-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 843-850.
    2. Wang, Junjie & Xiao, Aiguo, 2019. "Conservative Fourier spectral method and numerical investigation of space fractional Klein–Gordon–Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 348-365.
    3. Wang, Jun-jie & Xiao, Ai-guo, 2018. "An efficient conservative difference scheme for fractional Klein–Gordon–Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 691-709.
    4. Qin, Wendi & Ding, Deqiong & Ding, Xiaohua, 2015. "Two boundedness and monotonicity preserving methods for a generalized Fisher-KPP equation," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 552-567.
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    Cited by:

    1. Hu, Dongdong & Cai, Wenjun & Xu, Zhuangzhi & Bo, Yonghui & Wang, Yushun, 2021. "Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 35-59.

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