Faculty Publications

Permanent URI for this communityhttps://idr.nitk.ac.in/handle/123456789/18736

Publications by NITK Faculty

Browse

Author: search.filters.author.Sadananda, R.Subject: search.filters.subject.Fréchet derivative

Search Results

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    On the Order of Convergence of the Noor–Waseem Method
    (MDPI, 2022) George, S.; Sadananda, R.; Padikkal, J.; Argyros, I.K.
    In 2009, Noor and Waseem studied an important third-order iterative method. The convergenceorder is obtained using Taylor expansion and assumptions on the derivatives of order up tofour. In this paper, we have obtained convergence order three for this method using assumptionson the first and second derivatives of the involved operator. Further, we have extended the methodto obtain a fifth- and a sixth-order methods. The dynamics of the methods are also provided in thisstudy. Numerical examples are included. The same technique can be used to extend the utilization ofother single or multistep methods. © 2022 by the authors.
  • No Thumbnail Available
    Item
    Order of Convergence and Dynamics of Newton–Gauss-Type Methods
    (MDPI, 2023) Sadananda, R.; George, S.; Argyros, I.K.; Padikkal, J.
    On the basis of the new iterative technique designed by Zhongli Liu in 2016 with convergence orders of three and five, an extension to order six can be found in this paper. The study of high-convergence-order iterative methods under weak conditions is of extreme importance, because higher order means that fewer iterations are carried out to achieve a predetermined error tolerance. In order to enhance the practicality of these methods by Zhongli Liu, the convergence analysis is carried out without the application of Taylor expansion and requires the operator to be only two times differentiable, unlike the earlier studies. A semilocal convergence analysis is provided. Furthermore, numerical experiments verifying the convergence criteria, comparative studies and the dynamics are discussed for better interpretation. © 2023 by the authors.
  • No Thumbnail Available
    Item
    On the convergence of open Newton’s method
    (Springer Science and Business Media B.V., 2023) Kunnarath, A.; George, S.; Sadananda, R.; Padikkal, J.; Argyros, I.K.
    Cordero and Torregrosa proved the convergence of two Newton’s-like methods in 2007. Using Taylor expansion (requiring existence of derivatives of order up to four of the involved operator) they obtained the convergence order three for these methods. The convergence order three is obtained for Open Newton’s method and two extensions of it with assumptions only on first two derivatives of the operator involved. We verified the results with examples and dynamics of the results are presented. © 2023, The Author(s), under exclusive licence to The Forum D’Analystes.