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Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier

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  • Tomar, Saurabh
  • Singh, Mehakpreet
  • Vajravelu, Kuppalapalle
  • Ramos, Higinio

Abstract

The variational iteration method (VIM) has been in the last two decades, one of the most used semi-analytical techniques for approximating nonlinear differential equations. The notion of VIM is based on the identification of the Lagrange multiplier using the variational theory. The performance of the method is highly dependent on how the Lagrange multiplier is determined. In this paper, a novel method for calculating the Lagrange multiplier is provided, making the VIM more efficient in solving a variety of nonlinear problems. To illustrate the effectiveness of the new approach, a standard nonlinear oscillator problem is tested and the results demonstrate that only one iteration leads to an excellent outcome.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:640-644
    DOI: 10.1016/j.matcom.2022.09.003
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    References listed on IDEAS

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    1. Ahmad, Hijaz & Seadawy, Aly R. & Khan, Tufail A., 2020. "Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 13-23.
    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. Prakash, Amit & Kumar, Manoj & Sharma, Kapil K., 2015. "Numerical method for solving fractional coupled Burgers equations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 314-320.
    4. 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.
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    Cited by:

    1. Shirazian, Mohammad, 2023. "A new acceleration of variational iteration method for initial value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 246-259.

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