In this paper, we propose and discuss a new higher-order iterative method for solving nonlinear equations. This method based on a Halley and Householder iterative method and using predictor-corrector technique. The convergence analysis of our method is discussed. It is established that the new method has convergence order eighteen. Numerical tests show that the new method is comparable with the well-known existing methods and gives better results.

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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 PredictorCorrector 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.

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