On the Order of Convergence of the Noor–Waseem Method

Abstract

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.