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Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method

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  • Soliman, A.A.

Abstract

The solution for the generalized regularized long wave (for short, GRLW) equation based on variational iteratiom method, is exactly obtained. In this method, the solution is calculated in the form of convergent power series with easily computable componentes. This approach does need linearization, weak nonlinearity assumptions or perturbation theory. The results reveal that the method is very effective and convenient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:70:y:2005:i:2:p:119-124
    DOI: 10.1016/j.matcom.2005.06.002
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    Cited by:

    1. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
    2. Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
    3. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    4. Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
    5. Ali, A.H.A. & Raslan, K.R., 2009. "Variational iteration method for solving partial differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1520-1529.
    6. Li, Qi & Mei, Liquan, 2018. "Local momentum-preserving algorithms for the GRLW equation," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 77-92.
    7. Gao, Fuzheng & Qiao, Feng & Rui, Hongxing, 2015. "Numerical simulation of the modified regularized long wave equation by split least-squares mixed finite element method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 64-73.
    8. Karakoç, S. Battal Gazi & Zeybek, Halil, 2016. "Solitary-wave solutions of the GRLW equation using septic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 159-171.

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