Abstract
The recent paper [H. Ding, Y. Zhang, S. Wang, X. Yang,A note on some quadrature based three-step iterative methods for non-linear equations, Appl. Math. Comput.215 (1): (2009) 53--57] shows that the Algorithm 2.2 and Algorithm 2.3 in the article [N.A. Mir, T. Zaman, Somequadrature based three-step iterative methods for non-linear equations, Appl. Math. Comput. 193 (2):(2007) 366--373] have twelfth-order and ninth order convergence respectively, not seventh-order as claimed in the laterarticle. In this work; we propose two simple modifications, without increasing the computational cost or functionalevaluations, of the Algorithms 2.3 and 2.3. The first modification improves the convergence order of the Algorithm 2.3 fromninth-order to tenth order. In the second modification, we remove evaluation of the second derivative from the Algorithm2.2 while preserving its twelfth-order convergent nature.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
