IDEAS home Printed from https://ideas.repec.org/a/hin/jnljam/568740.html
   My bibliography  Save this article

A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order

Author

Listed:
  • F. Soleymani
  • S. Karimi Vanani
  • M. Jamali Paghaleh

Abstract

A class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle. Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning multipoint iterative methods without memory. Moreover, the class is free from derivative calculation per full iteration, which is important in engineering problems. One method of the class is established analytically. To test the derived methods from the class, we apply them to a lot of nonlinear scalar equations. Numerical examples suggest that the novel class of derivative-free methods is better than the existing methods of the same type in the literature.

Suggested Citation

  • F. Soleymani & S. Karimi Vanani & M. Jamali Paghaleh, 2012. "A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, February.
    • Handle: RePEc:hin:jnljam:568740
    DOI: 10.1155/2012/568740
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JAM/2012/568740.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JAM/2012/568740.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/568740?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. F. Soleymani, 2012. "Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, September.
    2. Jian Li & Xiaomeng Wang & Kalyanasundaram Madhu, 2019. "Higher-Order Derivative-Free Iterative Methods for Solving Nonlinear Equations and Their Basins of Attraction," Mathematics, MDPI, vol. 7(11), pages 1-15, 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:568740. 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.