Publication Type : Journal Article
Publisher : Springer Science and Business Media LLC
Source : The Journal of Analysis
Url : https://doi.org/10.1007/s41478-026-01113-w
Campus : Amritapuri
School : School of Physical Sciences
Department : Mathematics
Year : 2026
Abstract : This study examines the convergence behaviour of a fourth-order Newton-type iterative method for approximating locally unique solutions of nonlinear systems in Banach spaces. Although the method employs only first-order derivative information, existing convergence analyses frequently require assumptions on higher-order derivatives, which restrict its practical applicability. To address this issue, we establish both local and semilocal convergence results using conditions formulated solely in terms of the first derivative. Numerical experiments are presented to validate and demonstrate the theoretical findings.
Cite this Research Publication : Gopika Dinesh KC, Ioannis K. Argyros, Sreedeep Chekur Devadas, An improved two-step iterative method for solving systems of nonlinear equations, The Journal of Analysis, Springer Science and Business Media LLC, 2026, https://doi.org/10.1007/s41478-026-01113-w