IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v190y2021icp837-847.html
   My bibliography  Save this article

A splitting method to solve a single nonlinear equation with derivative-free iterative schemes

Author

Listed:
  • Liu, Chein-Shan
  • Hong, Hong-Ki
  • Lee, Tsung-Lin

Abstract

In the paper, we convert a single nonlinear equation to a system consisting of two equations. While a quasi-linear term is added on the first equation, the nonlinear term in the second equation is decomposed at two sides through a weight parameter. After performing a linearization, an iterative scheme is derived, which is proven of third-order convergence for certain parameters. An affine quasi-linear transformation in the plane is established, and the condition for the spectral radius being smaller than one for the convergence of the iterative scheme is derived. By using the splitting method, we can further identify a sufficient condition for the convergence of the iterative scheme. Then, we develop a step-wisely quasi-linear transformation technique to solve nonlinear equations. Proper values of the parameters are qualified by the derived inequalities for both iterative schemes, which accelerate the convergence speed. The performances of the proposed iterative schemes are assessed by numerical tests, whose advantages are fast convergence, saving the function evaluation per iteration and without needing the differential of the given function.

Suggested Citation

  • Liu, Chein-Shan & Hong, Hong-Ki & Lee, Tsung-Lin, 2021. "A splitting method to solve a single nonlinear equation with derivative-free iterative schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 837-847.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:837-847
    DOI: 10.1016/j.matcom.2021.06.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421002421
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.06.019?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. Chein-Shan Liu, 2020. "A New Splitting Technique for Solving Nonlinear Equations by an Iterative Scheme," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(4), pages 1-40, August.
    2. Muhammad Aslam Noor & Khalida Inayat Noor & Eisa Al-Said & Muhammad Waseem, 2010. "Some New Iterative Methods for Nonlinear Equations," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-12, January.
    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. Liu, Chein-Shan & Chen, Yung-Wei & Chang, Chih-Wen, 2024. "Precise eigenvalues in the solutions of generalized Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 354-373.
    2. Hu, Chaoming & Wan, Zhao Man & Zhu, Saihua & Wan, Zhong, 2022. "An integrated stochastic model and algorithm for constrained multi-item newsvendor problems by two-stage decision-making approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 280-300.
    3. Chein-Shan Liu, 2022. "Accurate Eigenvalues for the Sturm-Liouville Problems, Involving Generalized and Periodic Ones," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(4), pages 1-1, November.

    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. Chein-Shan Liu & Chih-Wen Chang, 2024. "Updating to Optimal Parametric Values by Memory-Dependent Methods: Iterative Schemes of Fractional Type for Solving Nonlinear Equations," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    2. Sania Qureshi & Higinio Ramos & Abdul Karim Soomro, 2021. "A New Nonlinear Ninth-Order Root-Finding Method with Error Analysis and Basins of Attraction," Mathematics, MDPI, vol. 9(16), pages 1-19, August.

    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:190:y:2021:i:c:p:837-847. 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.