IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i17p2785-d1474170.html
   My bibliography  Save this article

Accelerating the Speed of Convergence for High-Order Methods to Solve Equations

Author

Listed:
  • Ramandeep Behl

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

  • Ioannis K. Argyros

    (Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA)

  • Sattam Alharbi

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

Abstract

This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results.

Suggested Citation

  • Ramandeep Behl & Ioannis K. Argyros & Sattam Alharbi, 2024. "Accelerating the Speed of Convergence for High-Order Methods to Solve Equations," Mathematics, MDPI, vol. 12(17), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2785-:d:1474170
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/17/2785/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/17/2785/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xiao, Xiaoyong & Yin, Hongwei, 2015. "A new class of methods with higher order of convergence for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 300-309.
    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. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Sharma, Janak Raj & Sharma, Rajni & Bahl, Ashu, 2016. "An improved Newton–Traub composition for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 98-110.
    3. Xiao, Xiao-Yong & Yin, Hong-Wei, 2018. "Accelerating the convergence speed of iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 8-19.
    4. Ramandeep Behl & Ioannis K. Argyros & Sattam Alharbi, 2024. "A One-Parameter Family of Methods with a Higher Order of Convergence for Equations in a Banach Space," Mathematics, MDPI, vol. 12(9), pages 1-18, April.
    5. Bahl, Ashu & Cordero, Alicia & Sharma, Rajni & R. Torregrosa, Juan, 2019. "A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 147-166.

    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:12:y:2024:i:17:p:2785-:d:1474170. 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.