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A conservative linear difference scheme for the 2D regularized long-wave equation

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  • Wang, Xiaofeng
  • Dai, Weizhong
  • Guo, Shuangbing

Abstract

In the present work, a three-level in time linear and conservative implicit finite difference scheme for solving the 2D regularized long-wave equation is proposed. The existence, uniqueness, and conservations for mass and energy of the numerical solution are proved by the discrete energy method. The new scheme is shown to be second-order convergent and unconditionally stable. Numerical examples are provided to show the present scheme to be efficient and reliable.

Suggested Citation

  • Wang, Xiaofeng & Dai, Weizhong & Guo, Shuangbing, 2019. "A conservative linear difference scheme for the 2D regularized long-wave equation," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 55-70.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:55-70
    DOI: 10.1016/j.amc.2018.09.029
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    References listed on IDEAS

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    1. Atouani, Noureddine & Omrani, Khaled, 2015. "On the convergence of conservative difference schemes for the 2D generalized Rosenau–Korteweg de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 832-847.
    2. Hamdi, S. & Enright, W.H. & Schiesser, W.E & Gottlieb, J.J., 2004. "Exact solutions and invariants of motion for general types of regularized long wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(4), pages 535-545.
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    Cited by:

    1. Khater, Mostafa M.A., 2023. "Computational simulations of propagation of a tsunami wave across the ocean," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Dimitrienko, Yu.I. & Li, Shuguang & Niu, Yi, 2021. "Study on the dynamics of a nonlinear dispersion model in both 1D and 2D based on the fourth-order compact conservative difference scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 661-689.
    3. Wang, Xiaofeng & Dai, Weizhong & Guo, Shuangbing, 2021. "Corrigendum to “A conservative linear difference scheme for the 2D regularized long-wave equation” [Appl. Math. Comput. 342 (2019) 55–70]," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    4. Rouatbi, Asma & Omrani, Khaled, 2021. "Comments on the paper ”A conservative linear difference scheme for the 2D regularized long-wave equation”, by Xiaofeng Wang, Weizhong Dai and Shuangbing Guo [Applied Mathematics and Computation, 342 (," Applied Mathematics and Computation, Elsevier, vol. 410(C).

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