@article{Yu2025, 
author = {Li Yu and Xiaofeng Wang},
title = {Semi-local convergence of a sixth-order iterative method for solving nonlinear systems},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {6},
pages = {3794-3810},
keywords = {nonlinear equations, semi-local convergence, recurrence relation, domain of existence and uniqueness},
url = {https://www.sciopen.com/article/10.3934/era.2025168},
doi = {10.3934/era.2025168},
abstract = {This paper verifies the semi-local convergence of a sixth-order iterative method for solving nonlinear systems. In the proof, the recursive relation method is used to prove the semi-local convergence of the iterative method in Banach spaces. The proof process outlined above does not necessitate the higher-order continuous differentiability of the function    L  (  u  ). The advantage of the iterative method is that by employing auxiliary sequences and functions, convergence can be established using only first-order Fréchet derivatives. The proposed sixth-order method reduces computational costs compared to existing sixth-order methods by requiring only one LU decomposition per iteration instead of two. Finally, this sixth-order iterative approach is utilized for solving Hammerstein equations along with real gas equation of state. The experimental results prove the effectiveness of the iterative method.}
}