IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3146-d1195682.html
   My bibliography  Save this article

Efficient Fourth-Order Scheme for Multiple Zeros: Applications and Convergence Analysis in Real-Life and Academic Problems

Author

Listed:
  • Sunil Kumar

    (Department of Mathematics, University Centre for Research and Development, Chandigarh University, Mohali 140413, India)

  • Ramandeep Behl

    (Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Azizah Alrajhi

    (Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

High-order iterative techniques without derivatives for multiple roots have wide-ranging applications in the following: optimization tasks, where the objective function lacks explicit derivatives or is computationally expensive to evaluate; engineering; design finance; data science; and computational physics. The versatility and robustness of derivative-free fourth-order methods make them a valuable tool for tackling complex real-world optimization challenges. An optimal extension of the Traub–Steffensen technique for finding multiple roots is presented in this work. In contrast to past studies, the new expanded technique effectively handles functions with multiple zeros. In addition, a theorem is presented to analyze the convergence order of the proposed technique. We also examine the convergence analysis for four real-life problems, namely, Planck’s law radiation, Van der Waals, the Manning equation for isentropic supersonic flow, the blood rheology model, and two well-known academic problems. The efficiency of the approach and its convergence behavior are studied, providing valuable insights for practical and academic applications.

Suggested Citation

  • Sunil Kumar & Ramandeep Behl & Azizah Alrajhi, 2023. "Efficient Fourth-Order Scheme for Multiple Zeros: Applications and Convergence Analysis in Real-Life and Academic Problems," Mathematics, MDPI, vol. 11(14), pages 1-16, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3146-:d:1195682
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3146/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/14/3146/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ramandeep Behl & Samaher Khalaf Alharbi & Fouad Othman Mallawi & Mehdi Salimi, 2020. "An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    Full references (including those not matched with items on IDEAS)

    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. Ramandeep Behl, 2022. "A Derivative Free Fourth-Order Optimal Scheme for Applied Science Problems," Mathematics, MDPI, vol. 10(9), pages 1-17, April.

    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:gam:jmathe:v:11:y:2023:i:14:p:3146-:d:1195682. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.