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Local momentum-preserving algorithms for the GRLW equation

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  • Li, Qi
  • Mei, Liquan

Abstract

In this paper, four local momentum-preserving (LMP) algorithms for the GRLW equation are studied. The proposed algorithms, which conserve the local momentum conservation in any local time-space region, are proved to be momentum- and mass-preserving globally with appropriate boundary conditions. Two of the algorithms are explicit, and the other two are implicit. We make nonlinear convergence and stability analysis for the implicit algorithms. Numerical experiments confirm the long time preservation of the proposed algorithms and verify the theoretical analysis.

Suggested Citation

  • Li, Qi & Mei, Liquan, 2018. "Local momentum-preserving algorithms for the GRLW equation," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 77-92.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:77-92
    DOI: 10.1016/j.amc.2018.02.033
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    References listed on IDEAS

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    1. Hammad, D.A. & El-Azab, M.S., 2015. "A 2N order compact finite difference method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 248-261.
    2. Soliman, A.A., 2005. "Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(2), pages 119-124.
    3. Raslan, K.R., 2009. "Numerical study of the Modified Regularized Long Wave (MRLW) equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1845-1853.
    4. Hammad, D.A. & El-Azab, M.S., 2015. "2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burger’s–Fisher equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 296-311.
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