Open Journal of Mathematical Sciences
Vol. 8 (2024), Issue 1, pp. 39-45
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0224
On the semilocal convergence analysis of a seventh order four step method for solving nonlinear equations
Samundra Regmi\(^{1}\), Ioannis K. Argyros\(^{2,*}\), Santhosh George\(^{3}\) and Christopher I. Argyros\(^{4}\)
\(^{1}\) European Space Research and Technology Centre (ret.); Current address: Blue Abyss, Newquay, Cornwall, United Kingdom; Pletservladimir@gmail.com
Copyright © 2024 Samundra Regmi , Ioannis K. Argyros , Santhosh George and Christopher I. Argyros. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 19, 2022 – Accepted: April 06, 2024 – Published: June 30, 2024
Abstract
We provide a semi-local convergence analysis of a seventh order four step method for solving nonlinear problems. Using majorizing sequences and under conditions on the first derivative, we provide sufficient convergence criteria, error bounds on the distances involved and uniqueness. Earlier convergence results have used the eighth derivative not on this method to show convergence. Hence, limiting its applicability.
Keywords:
Banach space; convergence order; Iterative method.