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Application of variational iteration method to the generalized Burgers–Huxley equation

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  • Batiha, B.
  • Noorani, M.S.M.
  • Hashim, I.

Abstract

In this paper, He’s variational iteration method (VIM) is applied to the generalized Burgers–Huxley equation. The VIM produces an approximate solution of the equation without any discretization. The VIM is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. Comparisons with the Adomian decomposition method (ADM) reveal that the VIM is very effective and convenient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:660-663
    DOI: 10.1016/j.chaos.2006.06.080
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Limit cycle and bifurcation of nonlinear problems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 827-833.
    2. Abulwafa, E.M. & Abdou, M.A. & Mahmoud, A.A., 2006. "The solution of nonlinear coagulation problem with mass loss," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 313-330.
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    4. 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.
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    Cited by:

    1. Yadav, Swati & Pandey, Rajesh K., 2020. "Numerical approximation of fractional burgers equation with Atangana–Baleanu derivative in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Fesanghary, M. & Pirbodaghi, T. & Asghari, M. & Sojoudi, H., 2009. "A new analytical approximation to the Duffing-harmonic oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 571-576.
    3. Jaiswal, Shubham & Chopra, Manish & Das, S., 2019. "Numerical solution of non-linear partial differential equation for porous media using operational matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 138-154.
    4. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2152-2159.
    5. Korkut, Sıla Övgü, 2023. "An accurate and efficient numerical solution for the generalized Burgers–Huxley equation via Taylor wavelets method: Qualitative analyses and Applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 324-341.

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