The Research Of High-order Iterative Methods For Solving Nonlinear Equations

We maily discuss several new methods of the solution of nonlinear equa-tions in this paper, which include a new Jarratt iteration method and two new arithmetic average Newton iteration methods and two new seven order iterative methods.Several numerical examples are given to illustrate the performance of the presented methods. This paper is divided into five chapters.The first chapter mainly introduces the research background, research con-tents, and some concepts and theorems which are involved in this paper.In the second chapter, we present a kind of Jarratt’s fourth-order method for solving nonlinear equations. It is shown that the order of convergence is improved from four to six even though it adds on evaluation of the function at the point interated by Jarratt’s method per iteration.In the third chapter, we present two arithmetic average Newton iteration methods for solving nonlinear equations. It is shown that the order of convergence is improved from three to five and six even though it adds on evaluation of the function at the point interated by arithmetic average Newton iteration method per iteration.In the fourth chapter, we present two new iterative methods which can solve nonlinear equations. It is shown that the order of convergence is improved from five to seven even though it adds on evaluation of the function at the point interated by per iteration.In the fifth chapter, we make simple summary for this thesis and point out the deficiency of this thesis as well as prospects for future research.