IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v204y2023icp640-644.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542200369X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.09.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xu, Lan, 2009. "The variational iteration method for fourth order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1386-1394.
    2. 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.
    3. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    4. Roman Parovik, 2020. "Mathematical Modeling of Linear Fractional Oscillators," Mathematics, MDPI, vol. 8(11), pages 1-26, October.
    5. 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.
    6. Mamta Kapoor & Nehad Ali Shah & Salman Saleem & Wajaree Weera, 2022. "An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    7. Deng, Hongmin & Li, Tao & Wang, Qionghua & Li, Hongbin, 2009. "A fractional-order hyperchaotic system and its synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 962-969.
    8. 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.
    9. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    10. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    11. Marwan Abukhaled, 2013. "Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology," Journal of Mathematics, Hindawi, vol. 2013, pages 1-4, February.
    12. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "A numeric–analytic method for approximating the chaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1784-1791.
    13. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
    14. Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
    15. Chun, Changbum, 2007. "Integration using He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1130-1134.
    16. Yu, Yongguang & Li, Han-Xiong, 2008. "The synchronization of fractional-order Rössler hyperchaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1393-1403.
    17. Kateryna Marynets, 2021. "Successive Approximation Technique in the Study of a Nonlinear Fractional Boundary Value Problem," Mathematics, MDPI, vol. 9(7), pages 1-19, March.
    18. Odibat, Zaid M., 2009. "Computational algorithms for computing the fractional derivatives of functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2013-2020.
    19. Rehman, Mujeeb ur & Idrees, Amna & Saeed, Umer, 2017. "A quadrature method for numerical solutions of fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 38-49.
    20. Neslihan Ozdemir & Aydin Secer & Mustafa Bayram, 2019. "The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative," Mathematics, MDPI, vol. 7(6), pages 1-15, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:640-644. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.