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A new local energy-preserving algorithm for the BBM equation

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  • Yang, Yanhong
  • Wang, Yushun
  • Song, Yongzhong

Abstract

In this paper, a new local energy-preserving algorithm is proposed based on the temporal and spatial discretizations where the Average Vector Field (AVF) method and the implicit midpoint method are used for the temporal discretization and spatial discretization, respectively. In any local time-space region, the local mass and local energy are conserved by the algorithm. With periodic boundary conditions, it is worth noting that the global mass and global energy conservation law are also admitted. Numerical experiments are performed to support our theoretical analysis and show the conservation properties of the algorithm intuitively.

Suggested Citation

  • Yang, Yanhong & Wang, Yushun & Song, Yongzhong, 2018. "A new local energy-preserving algorithm for the BBM equation," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 119-130.
    • Handle: RePEc:eee:apmaco:v:324:y:2018:i:c:p:119-130
    DOI: 10.1016/j.amc.2017.12.013
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    References listed on IDEAS

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    1. Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2015. "Energy conservation issues in the numerical solution of the semilinear wave equation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 842-870.
    2. Wazwaz, Abdul-Majid & Helal, M.A., 2005. "Nonlinear variants of the BBM equation with compact and noncompact physical structures," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 767-776.
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    Cited by:

    1. You, Xiangcheng & Xu, Hang & Sun, Qiang, 2022. "Analysis of BBM solitary wave interactions using the conserved quantities," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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