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Application of He’s variational iteration method to Helmholtz equation

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  • Momani, Shaher
  • Abuasad, Salah

Abstract

In this article, we implement a new analytical technique, He’s variational iteration method for solving the linear Helmholtz partial differential equation. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via the variational theory. The initial approximations can be freely chosen with possible unknown constants, which can be determined by imposing the boundary/initial conditions. The results compare well with those obtained by the Adomian’s decomposition method.

Suggested Citation

  • Momani, Shaher & Abuasad, Salah, 2006. "Application of He’s variational iteration method to Helmholtz equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1119-1123.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:5:p:1119-1123
    DOI: 10.1016/j.chaos.2005.04.113
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    Citations

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    Cited by:

    1. Tatari, Mehdi & Dehghan, Mehdi, 2007. "He’s variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 671-677.
    2. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    3. Tomar, Saurabh & Singh, Mehakpreet & Vajravelu, Kuppalapalle & Ramos, Higinio, 2023. "Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 640-644.
    4. Gordoa, P.R., 2007. "A note on solutions of an equation modelling arterial deformation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1505-1511.
    5. Chun, Changbum, 2007. "Integration using He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1130-1134.
    6. Xu, Lan, 2009. "The variational iteration method for fourth order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1386-1394.
    7. Marinca, Vasile & Herişanu, Nicolae, 2008. "Periodic solutions of Duffing equation with strong non-linearity," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 144-149.
    8. 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.
    9. 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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