Construction of Iterative Families Based on Power Means

Abstract

Nonlinear equations appear in many disciplines of sciences such as engineering, mathematics, robotics and computer sciences because majority of physical systems are nonlinear in nature. One of the most basic and challenging tasks is to find the solution to nonlinear equations effectively and accurately. In this study, we provide and analyze some new iterative techniques for solving non-linear equations. The thesis consists of four chapters as follows: CHAPTER 1: In this chapter, some basic concepts and definitions regarding the non-linear equations are introduced. Some fundamental concepts of calculus are also explained in this chapter. Further, a brief explanation of classical iterative methods is provided which are commonly used in scientific and engineering problems. CHAPTER 2: It provides a survey of the work proposed by Lotfi et al.[1] in year 2014. Which deals with efficient iterative methods with and without memory possessing high efficiency indices. CHAPTER 3: In this chapter, new optimal iterative derivative free families based on power-mean are constructed. The proposed families give several with and without memory iterative methods having higher order of convergence. CHAPTER 4: Numerical comparisons of proposed methods with some other same order iterative methods have been performed in this chapter. The numerical results are illustrate the theoretical aspects using the programming package Mathematica 10.