Newton Type Numerical Methods for Solving Nonlinear Equations

Abstract

Nonlinear equations arise in almost all areas of sciences, in particular, in physical and mathematical sciences. Practically, it is rarely possible to solve a nonlinear equation analytically. So, iterative methods are generally employed in such situations. The most common among such methods for solving a nonlinear equation f(x) = 0 are the Newton method and the secant method. newline newlineIt is known that the order of convergence of Newton method is 2 while that of newlinesecant method is 1.618. newlineOver the years, tremendous variants of these methods have appeared showing newlineone or the other advantages over these methods in some sense. Some of newlinethe recent work in this direction include [39], [49]-[59], [41], [76], [80]. We aim newlineat contributing further in this direction. newlineThe thesis as such is divided into six chapters (Chapter 1 to Chapter 6). newlineChapter 1 is preliminary in nature where we include known definitions, concepts newlineand results which are required in the subsequent chapters. In rest of the newlinechapters, i.e., Chapter 2 to Chapter 6, we include our own findings. We give newlinebelow a brief description of each of the chapters.