High convergence order iterative method for nonlinear system of equations in Banach spaces

In this work, an efficient eighth-order iterative method is proposed for solving systems of nonlinear equations in Banach spaces. The local convergence is analyzed by assuming weaker omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document}-continuity condition on first order Fr & eacute;chet derivative which thus expands the applicability of the method for such problems where the earlier study based on Lipschitz or H & ouml;lder conditions cannot be used. Computational Efficiency of the proposed scheme is studied and compared with existing iterative methods. Numerical experiments are performed on a variety of real life problems including Kepler's equation, Van der waals equation of state, mixed Hammerstein-type equation etc. and comparison results are corroborated to extend the utility of presented method.