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A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations

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  • Soliman, A.A.

Abstract

By means of variational iteration method the solution of the Korteweg-de Vries Burgers (for short, KdVB) and a Lax’s seventh-order KdV (for short, LsKdV) equations are exactly obtained and in compared with that found by means of Adomian decomposition method. The comparison demonstrate that the two obtained solutions are an excellent agreement. The numerical results calculated and show that this method, variational iteration method, can be readily implemented to this type of nonlinear equations and excellent accuracy can be also achieved. The results of variation iteration method confirm the correctness of those obtained by mean of Adomian decomposition method.

Suggested Citation

  • Soliman, A.A., 2006. "A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 294-302.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:294-302
    DOI: 10.1016/j.chaos.2005.08.054
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    Cited by:

    1. Javidi, M. & Golbabai, A., 2009. "A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 849-857.
    2. Dehghan, Mehdi & Tatari, Mehdi, 2008. "Identifying an unknown function in a parabolic equation with overspecified data via He’s variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 157-166.
    3. Batiha, B. & Noorani, M.S.M. & Hashim, I., 2008. "Application of variational iteration method to the generalized Burgers–Huxley equation," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 660-663.
    4. 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.
    5. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    6. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.

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