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On the Order of Convergence of the Noor–Waseem Method

Author

Listed:
  • Santhosh George

    (Department of Mathematical & Computational Science, National Institute of Technology Karnataka, Surathkal 575 025, India)

  • Ramya Sadananda

    (Department of Mathematical & Computational Science, National Institute of Technology Karnataka, Surathkal 575 025, India)

  • Jidesh Padikkal

    (Department of Mathematical & Computational Science, National Institute of Technology Karnataka, Surathkal 575 025, India)

  • Ioannis K. Argyros

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

Abstract

In 2009, Noor and Waseem studied an important third-order iterative method. The convergence order is obtained using Taylor expansion and assumptions on the derivatives of order up to four. In this paper, we have obtained convergence order three for this method using assumptions on the first and second derivatives of the involved operator. Further, we have extended the method to obtain a fifth- and a sixth-order methods. The dynamics of the methods are also provided in this study. Numerical examples are included. The same technique can be used to extend the utilization of other single or multistep methods.

Suggested Citation

  • Santhosh George & Ramya Sadananda & Jidesh Padikkal & Ioannis K. Argyros, 2022. "On the Order of Convergence of the Noor–Waseem Method," Mathematics, MDPI, vol. 10(23), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4544-:d:990156
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