Convergence Analysis of Higher Order Iterative Methods in Banach Spaces

Abstract

newline This thesis is devoted to the study of convergence analysis of higher order iterative newlinemethods used to approximate a unique zero of the non-linear operator G in B- newlinespaces (Banach spaces). To finding solution of non-linear operator in the area of newlinecomputational sciences such as transportation, chemical engineering, operational newlineresearch, kinetic theory and many other branches in applied mathematics which newlineinvolves system of linear, non-linear equation, differential equation, functional newlineequation, integral equation, boundary value problem etc. Many optimization newlineproblems are also been studied for solving such types of equations. For finding newlinezeros of these equations we used numerical methods which are known as iterative newlinemethod. There are many iterative methods like Bisection, Secant, Newton, Halley, newlineChebyshev, Super-Halley, Chebyshev-Halley, modified Newton-like and so on. newlineGenerally, before choosing a method for finding zero of non-linear operator, it newlineis most important to study the convergence analysis of the method. The study newlineof convergence mostly based on two types which are local and semi-local. Many newlineauthors like Kantorovich, Chen, Yamamoto, Argyros, George, Candela, Marquina, newlineSmale, Guti´ errez, Hernández worked on to study the convergence of such iterative newlinemethods using various conditions such as majorant, recurrence, etc in B-space. In newline2012, Argyros and Ren [23] and in 2014, Ling and Ku [104] provided local and semi- newlinelocal convergence analysis of the Halley s method under second order derivative newlineof majorant conditions in B-spaces.