الفهرس 
General IntroductionOnly 14 pages are availabe for public view
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Abstract
This study aimed to present several proposed iterative methods for the solution of nonlinear equation of multiple roots and avoiding most of the drawbacks. The computational examples in this thesis were done with Maple 18. This thesis, which consists of four basic chapters, is concerned with analytical and numerical study for solving nonlinear algebraic Equations of multiple roots.
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 with single root and multiple roots throughout the next chapters are presented. All the numerical concepts and definitions which are used in this study, are given.
Chapter 2: In this chapter, the proposed iterative relations for solving nonlinear equations with multiple roots have been introduced. their order of convergence for each relations are analyzed and proved, the convergence analysis proves our proposed iterative methods preserve their order of convergence. Some numerical examples demonstrate that the proposed iterative relations are efficiency index. For the special case which the multiplicity of the roots of nonlinear equation is a single multiplicity, the methods are more efficiency and performs better than many other existing relations. Unfortunately, our presented relations require two and three iteration steps to obtain the desired precisions while the others methods require more than three steps. The efficiency index of some proposed relations such as Relation 2.2.3 and Relation 2.2.4 is 1.587, this shows the proposed methods are of good efficiency index.
Chapter 3: In this chapter, a new family of iterative relations for finding multiple rootsn of nonlinear equations are constructed. It is proved that these relations have the convergence order of four, six, and nine, the most of new family of the relations reaches the optimal order of convergence nine which is higher than Newton’s method and others. The order of convergence for each method is analyzed and proved. Results for some numerical examples show the efficiency index of the proposed relations.
Chapter 4: In this chapter, we have suggested some iterative methods for obtaining multiple roots of nonlinear equations by using variational iteration technique. The suggested methods have significance that these methods can be applied when multiplicity of the root is not known. from the numerical examples, it is clear that all the methods introduced in this chapter perform better than the modified Newton’s method for obtaining multiple roots of nonlinear equations. Using the technique and idea, one can suggest and analyze higher order iterative methods for solving nonlinear equations as well as system of nonlinear equations. We have also studied the convergence analysis of the general iterative method. Several special cases are also considered. The results obtained in this may stimulate further research in this field.