الفهرس 
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Abstract
In this study the researcher will present several iterative for studying for solving the nonlinear equation and avoiding most of the drawbacks. Variety of the numerical methods is used to study the solution of nonlinear equations. The computational examples in this thesis were done with Maple 14. This thesis, consists of four basic chapters and two Appendices, is concerned with analytical and numerical study for solving non-linear algebraic equations.
Chapter 1: The researcher gives a brief introduction to nonlinear equations. Most of the basic concepts are overviews, theorems and the mathematical tools that we use throughout the next chapters are presented. All the numerical concepts, definitions which are used in this study, are given.
Chapter 2: In this chapter, we improve the order of convergence of the one and two-step iterative methods for solving nonlinear equations by higher-order family of three-step iterative methods with double-Newton’s methods. The six proposed methods of convergence orders five, six, six, ten, twelve and eighteen. We will demonstrate the order of convergence of the proposed methods. Computational results are given to prove that the methods of the three-step are efficient and exhibit equal or better performance as compared with other well known methods and the classical Newton’s method.
Chapter 3: In this chapter, we suggest and analyze some new higher-order iterative methods free from derivatives that are used for solving nonlinear equations =0. The forward difference formula for approximating the first derivative of also gives several examples to illustrate the efficiency of these methods. Comparison with other similar method is also given. These new methods can be considered as alternative to the developed methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations. The methods of the three-step are efficient and exhibit equal or better performance as compared with other well known methods and the classical Newton’s method.
Chapter 4: In this chapter, we suggest and analyze some new higher-order iterative methods free from derivatives and use it for solving nonlinear equations =0 using the cental difference formula for approximating the first derivative of . We also give several examples to illustrate the efficiency of these methods. Comparison with other similar method is also given. These new methods can be considered as alternative to the developed methods.