@article{Ali2026, 
author = {Ali Hasan Ali and Iman A. Abdul Samad and Huda J. Saeed and Firas Ghanim and Alina Alb Lupaș},
title = {Predictor-corrector higher derivative-free algorithms for nonlinear equations with basin of attraction analysis},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {16550-16569},
keywords = {quadrature rule, Adomian decomposition approach, iterative methods, basins of attraction, numerical analysis},
url = {https://www.sciopen.com/article/10.3934/math.2026679},
doi = {10.3934/math.2026679},
abstract = {This work presents two new numerical methods for finding the zeros of nonlinear equations, based on the Adomian decomposition approach and the quadrature rule. Using a predictor–corrector scheme, the proposed iterative methods provide a high order of convergence and do not require second derivatives, thereby reducing computational time. The methods are tested on several functions, and their efficiency is demonstrated through comparisons with various established techniques. To support the numerical findings, graphical analyses are provided. Furthermore, a study of the basins of attraction is conducted to validate the stability of the proposed methods.}
}