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

Saurabh Tomar, Mehakpreet Singh, Kuppalapalle Vajravelu and Higinio Ramos

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 204, issue C, 640-644

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.

Keywords: Variational iteration method; Variational principle; Lagrange multiplier; Nonlinear oscillator (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:204:y:2023:i:c:p:640-644

DOI: 10.1016/j.matcom.2022.09.003

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