IDEAS home Printed from https://ideas.repec.org/a/hin/jnljam/539707.html
   My bibliography  Save this article

Basins of Attraction for Various Steffensen-Type Methods

Author

Listed:
  • Alicia Cordero
  • Fazlollah Soleymani
  • Juan R. Torregrosa
  • Stanford Shateyi

Abstract

The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package M ATHEMATICA provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.

Suggested Citation

  • Alicia Cordero & Fazlollah Soleymani & Juan R. Torregrosa & Stanford Shateyi, 2014. "Basins of Attraction for Various Steffensen-Type Methods," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-17, March.
    • Handle: RePEc:hin:jnljam:539707
    DOI: 10.1155/2014/539707
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JAM/2014/539707.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JAM/2014/539707.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/539707?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Anuradha Singh & J. P. Jaiswal, 2014. "An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics," Journal of Mathematics, Hindawi, vol. 2014, pages 1-14, September.
    2. Beny Neta, 2021. "A Note on Traub’s Method for Systems of Nonlinear Equations," Mathematics, MDPI, vol. 9(23), pages 1-8, November.
    3. Mihael Baketarić & Marjan Mernik & Tomaž Kosar, 2021. "Attraction Basins in Metaheuristics: A Systematic Mapping Study," Mathematics, MDPI, vol. 9(23), pages 1-25, November.

    More about this item

    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:hin:jnljam:539707. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.