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The use of adomian decomposition method for solving the regularized long-wave equation

Author

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  • El-Danaf, Talaat S.
  • Ramadan, Mohamed A.
  • Abd Alaal, Faysal E.I.

Abstract

In this paper, an accurate method to obtain an approximate numerical solution for the nonlinear regularized long-wave (in short RLW) equation is considered. The theoretical analysis of the method is investigated. The performance and the accuracy of the algorithm are illustrated by solving two test examples of the problem. The obtained results are presented and compared with the analytical solutions. It is observed that only few terms of the series expansion are required to obtain approximate solutions with good accuracy.

Suggested Citation

  • El-Danaf, Talaat S. & Ramadan, Mohamed A. & Abd Alaal, Faysal E.I., 2005. "The use of adomian decomposition method for solving the regularized long-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 747-757.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:747-757
    DOI: 10.1016/j.chaos.2005.02.012
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    Cited by:

    1. Abourabia, A.M. & El-Danaf, T.S. & Morad, A.M., 2009. "Exact solutions of the hierarchical Korteweg–de Vries equation of microstructured granular materials," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 716-726.
    2. Wang, Yue-yue & Dai, Chao-qing & Wu, Lei & Zhang, Jie-fang, 2007. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1208-1214.
    3. 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.
    4. Elgazery, Nasser S., 2008. "Numerical solution for the Falkner–Skan equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 738-746.
    5. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    6. Ramos, J.I., 2007. "Solitary waves of the EW and RLW equations," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1498-1518.
    7. Tajvidi, T. & Razzaghi, M. & Dehghan, M., 2008. "Modified rational Legendre approach to laminar viscous flow over a semi-infinite flat plate," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 59-66.
    8. Abourabia, Aly M. & Hassan, Kawsar M. & Morad, Adel M., 2009. "Analytical solutions of the magma equations for molten rocks in a granular matrix," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1170-1180.
    9. Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
    10. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    11. Hammad, D.A. & El-Azab, M.S., 2016. "Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 228-240.
    12. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    13. Dehghan, Mehdi & Shakourifar, Mohammad & Hamidi, Asgar, 2009. "The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2509-2521.
    14. Yuzhen Chai & Tingting Jia & Huiqin Hao & Jianwen Zhang, 2014. "Exp-Function Method for a Generalized MKdV Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, May.
    15. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    16. Asma Rouatbi & Manel Labidi & Khaled Omrani, 2020. "Conservative Difference Scheme of Solitary Wave Solutions of the Generalized Regularized Long-Wave Equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1317-1342, December.
    17. Raslan, K.R., 2009. "Numerical study of the Modified Regularized Long Wave (MRLW) equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1845-1853.

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