To Explore Iterative Methods For Solving Systems Of Nonlinear Equations

Solving the system of nonlinear equations is an important topic in Computational Mathematics. With the increasing development of science and technology, iterative methods for solving nonlinear equations are constantly updated, and various kinds of high order, and efficient methods continue to be raised. In this thesis we construct several iterative schemes to solve the system of nonlinear equations. The main contributions include:Firstly, we derive a new iterative method, which is based on Newton and Chebyshev iteration, to solve the system of nonlinear equations with order of convergence higher than other competitive methods. Numerical examples are given to show that the proposed method outperforms the existing methods in that it has less iterations.Secondly, we derive a new iterative method of order five to solve the system of nonlinear equations. The new method is based on the two-step iterative method of order three proposed by Sharma and Gupta. Numerical examples are given to show that the proposed method has higher efficiency than others. The efficiency index is used to compare the efficiency of the new method with those of other ones, and the test reveals that the presented method has great advantage, when n≥2.Thirdly, we present a new iterative method to solve systems of nonlinear equations, and prove its convergence. Numerical examples are given to show that our method, compared with Newton’s method, fourth-order method and fifth-order method by A.Cordero, has a significant improvement. And comparing the presented method and the above mentioned three methods in terms of efficiency index reveals that our method is of great advantage when n≥2.