IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v505y2025ics0096300325002528.html

Local and semilocal analysis of a class of fourth order methods under common set of assumptions

Author

Listed:
  • Kunnarath, Ajil
  • George, Santhosh
  • Jidesh, P.

Abstract

This study presents an efficient class of fourth-order iterative methods introduced by Ali Zein (2024) in a more abstract Banach space setting. The Convergence Order of this class is proved by bypassing the Taylor expansion. We use the mean value theorem and relax the differentiability assumptions of the involved function. At the outset, we provide a semilocal analysis, and then, using the results and the same set of assumptions, we study the local convergence. This approach has the advantage that we do not need to use any assumptions on the unknown solution to study the local convergence. This technique can be used to extend the applicability of other methods along the same lines. Examples from both the chemical and the physical sciences are studied to analyze the performance of the class. The dynamics of the class are also studied.

Suggested Citation

  • Kunnarath, Ajil & George, Santhosh & Jidesh, P., 2025. "Local and semilocal analysis of a class of fourth order methods under common set of assumptions," Applied Mathematics and Computation, Elsevier, vol. 505(C).
    • Handle: RePEc:eee:apmaco:v:505:y:2025:i:c:s0096300325002528
    DOI: 10.1016/j.amc.2025.129526
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325002528
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129526?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Kalyanasundaram Madhu & Jayakumar Jayaraman, 2016. "Higher Order Methods for Nonlinear Equations and Their Basins of Attraction," Mathematics, MDPI, vol. 4(2), pages 1-20, April.
    2. J. P. Jaiswal, 2014. "Some Class of Third‐ and Fourth‐Order Iterative Methods for Solving Nonlinear Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. J. P. Jaiswal, 2014. "Some Class of Third- and Fourth-Order Iterative Methods for Solving Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-17, May.
    4. Ali Zein & Chong Lin, 2024. "A New Family of Optimal Fourth-Order Iterative Methods for Solving Nonlinear Equations With Applications," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-22, October.
    5. Rajni Sharma & Ashu Bahl, 2015. "An Optimal Fourth Order Iterative Method for Solving Nonlinear Equations and Its Dynamics," Journal of Complex Analysis, Hindawi, vol. 2015, pages 1-9, November.
    6. Ramandeep Behl & Munish Kansal & Mehdi Salimi, 2020. "Modified King’s Family for Multiple Zeros of Scalar Nonlinear Functions," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    7. Alzahrani, Abdullah Khamis Hassan & Behl, Ramandeep & Alshomrani, Ali Saleh, 2018. "Some higher-order iteration functions for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 80-93.
    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. Sagar, Prem & Sharma, Janak Raj, 2026. "An extension of Ostrowski’s method with improved convergence and complex geometry," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 238-256.

    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. Mohammed Barrada & Mariya Ouaissa & Yassine Rhazali & Mariyam Ouaissa, 2020. "A New Class of Halley’s Method with Third‐Order Convergence for Solving Nonlinear Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    2. Liu, Dongjie & Liu, Chein-Shan, 2022. "Two-point generalized Hermite interpolation: Double-weight function and functional recursion methods for solving nonlinear equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 317-330.
    3. Sagar, Prem & Sharma, Janak Raj, 2026. "An extension of Ostrowski’s method with improved convergence and complex geometry," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 238-256.
    4. Prem B. Chand & Francisco I. Chicharro & Neus Garrido & Pankaj Jain, 2019. "Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications," Mathematics, MDPI, vol. 7(10), pages 1-21, October.
    5. José J. Padilla & Francisco I. Chicharro & Alicia Cordero & Alejandro M. Hernández-Díaz & Juan R. Torregrosa, 2024. "A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam," Mathematics, MDPI, vol. 12(3), pages 1-16, February.
    6. Hessah Faihan Alqahtani & Ramandeep Behl & Munish Kansal, 2019. "Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    7. Yanlin Tao & Kalyanasundaram Madhu, 2019. "Optimal Fourth, Eighth and Sixteenth Order Methods by Using Divided Difference Techniques and Their Basins of Attraction and Its Application," Mathematics, MDPI, vol. 7(4), pages 1-22, March.
    8. Deepak Kumar & Ioannis K. Argyros & Janak Raj Sharma, 2018. "Convergence Ball and Complex Geometry of an Iteration Function of Higher Order," Mathematics, MDPI, vol. 7(1), pages 1-13, December.
    9. Alemu Senbeta Bekela & Alemayehu Tamirie Deresse, 2025. "An Efficient Numerical Method for Nonlinear Time Fractional Hyperbolic Partial Differential Equations Based on Fractional Shehu Transform Iterative Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    10. Janak Raj Sharma & Deepak Kumar & Ioannis K. Argyros, 2019. "Local Convergence and Attraction Basins of Higher Order, Jarratt-Like Iterations," Mathematics, MDPI, vol. 7(12), pages 1-16, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:apmaco:v:505:y:2025:i:c:s0096300325002528. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.