IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v12y2020i6p50.html
   My bibliography  Save this article

An Improved Secant Algorithm of Variable Order to Solve Nonlinear Equations Based on the Disassociation of Numerical Approximations and Iterative Progression

Author

Listed:
  • Christian Vanhille

Abstract

We propose an iterative method to evaluate the roots of nonlinear equations. This Secant-based technique approximates the derivatives of the function numerically through a constant discretization step h disassociated from the iterative progression. The algorithm is developed, implemented, and tested. Its order of convergence is found to be h-dependent. The results obtained corroborate the theoretical deductions and evidence its excellent behavior. For infinitesimal h-values, the algorithm accelerates the convergence of the Secant method to order 2 (the one of the Newton-Raphson method) with no need for analytic expression of derivatives (the advantage of the Secant method).

Suggested Citation

  • Christian Vanhille, 2020. "An Improved Secant Algorithm of Variable Order to Solve Nonlinear Equations Based on the Disassociation of Numerical Approximations and Iterative Progression," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(6), pages 1-50, December.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:6:p:50
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/download/0/0/44066/46681
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/0/44066
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shin Min Kang & Arif Rafiq & Young Chel Kwun, 2013. "A New Second-Order Iteration Method for Solving Nonlinear Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-4, April.
    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.

      More about this item

      JEL classification:

      • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
      • Z0 - Other Special Topics - - General

      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:ibn:jmrjnl:v:12:y:2020:i:6:p:50. 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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

      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.