On the Order of Convergence of the Noor–Waseem Method

Santhosh George, Ramya Sadananda, Jidesh Padikkal and Ioannis K. Argyros ()
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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

Mathematics, 2022, vol. 10, issue 23, 1-14

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.

Keywords: Noor–Waseem method; Taylor expansion; Fréchet derivative; order of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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