M.Q. Khirallah, M.A. Hafiz, Novel Three Order Methods for Solving a System of Nonlinear Equations, BMSA Volume 2, Bulletin of Mathematical Sciences and Applications (Volume 2)
https://www.scipress.com/BMSA.2.1
Abstract:
    In this paper, we suggest and study Simpson's formula, and Newton's two, three and four Cosed formulas iterative methods for solving the system of nonlinear equations by using Predictor-Corrector of Newton method. We present four new algorithms for solving the system of nonlinear equations (SNLE). We prove that these new algorithms have convergence. Several numerical examples are given to illustrate the efficiency and performance of the new iterative methods. These new algorithms may be viewed as an extensions and generalizations of the existing methods for solving the system of nonlinear equations.
Keywords:
    Predictor-Corrector Methods, Quadrature Formulas, System of Non-Linear Equations (SNLE)