IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3602-d931807.html
   My bibliography  Save this article

The Dynamics of a Continuous Newton-like Method

Author

Listed:
  • Manoj K. Singh

    (College of Technology, Sardar Vallabhbhai Patel University of Agriculture and Technology, Meerut 250110, India)

  • Ioannis K. Argyros

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

Abstract

The objective of the current work is to invent and introduce the continuous version of Newton’s method. This scheme is used to establish some interesting properties with examples. We have plotted the fractal pattern graphs for a Newton-like method and a Damped Newton-like method in the discrete case and hence we have introduced a new concept of streamline for the continuous version of the Newton-like method. The graph and streamlines of these patterns are in agreement with numerical results and describe the convergence and stability of the proposed method to different roots when the Newton method fails.

Suggested Citation

  • Manoj K. Singh & Ioannis K. Argyros, 2022. "The Dynamics of a Continuous Newton-like Method," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3602-:d:931807
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3602/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3602/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Manoj Kumar Singh & Arvind K. Singh, 2021. "The Optimal Order Newton’s Like Methods with Dynamics," Mathematics, MDPI, vol. 9(5), pages 1-24, March.
    2. Ioannis K. Argyros, 2021. "Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    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. Chein-Shan Liu & Chih-Wen Chang, 2024. "New Memory-Updating Methods in Two-Step Newton’s Variants for Solving Nonlinear Equations with High Efficiency Index," Mathematics, MDPI, vol. 12(4), pages 1-22, February.

    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. Samundra Regmi & Ioannis K. Argyros & Santhosh George & Michael I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
    2. Santhosh George & Jidesh Padikkal & Krishnendu Remesh & Ioannis K. Argyros, 2022. "A New Parameter Choice Strategy for Lavrentiev Regularization Method for Nonlinear Ill-Posed Equations," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    3. Ioannis K. Argyros & Samundra Regmi & Stepan Shakhno & Halyna Yarmola, 2022. "A Methodology for Obtaining the Different Convergence Orders of Numerical Method under Weaker Conditions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    4. Michael I. Argyros & Ioannis K. Argyros & Samundra Regmi & Santhosh George, 2022. "Generalized Three-Step Numerical Methods for Solving Equations in Banach Spaces," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    5. Samundra Regmi & Ioannis K. Argyros & Santhosh George & Christopher I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton-Kantorovich Iterations," Mathematics, MDPI, vol. 10(8), pages 1-14, April.
    6. Janak Raj Sharma & Harmandeep Singh & Ioannis K. Argyros, 2022. "A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces," Mathematics, MDPI, vol. 10(17), pages 1-16, September.
    7. Ioannis K. Argyros & Christopher Argyros & Johan Ceballos & Daniel González, 2022. "Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    8. Arseny A. Sorokin & Gerd Leuchs & Joel F. Corney & Nikolay A. Kalinin & Elena A. Anashkina & Alexey V. Andrianov, 2022. "Towards Quantum Noise Squeezing for 2-Micron Light with Tellurite and Chalcogenide Fibers with Large Kerr Nonlinearity," Mathematics, MDPI, vol. 10(19), pages 1-11, September.
    9. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi & Samaher Khalaf Alharbi, 2022. "Extending the Applicability of Highly Efficient Iterative Methods for Nonlinear Equations and Their Applications," Mathematics, MDPI, vol. 11(1), pages 1-18, December.

    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:10:y:2022:i:19:p:3602-:d:931807. 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.