Newton Type Iterative Methods for Solving Nonlinear Equations

Abstract

Solving single variable nonlinear equations efficiently is an important consideration in numerical analysis and has wide range of applications in all elds of science and engineering. Finding the analytic solutions of such equations is not always possible. Newton's method is the most widely used numerical method for solving such equations. In this thesis, we have developed several new Newton type iterative methods for solving nonlinear equations of a single variable. To obtain these methods, we used different techniques such as: (i) amalgamation of existing methods; (ii) amalgamation of existing and our investigated methods with the secant method; (iii) amalgamation of existing methods and modi ed secant method; (iv) idea of integral approximation; and (v) use of inverse function methods. The work done in this thesis is inspired by the work of Potra and Pt ak, Kasturiarachi, Jain, Weerakon and Fernando, Ozban, Dhegain and Hajarian, Ujevi c, Erceg and Laki c, Amit and Basqular, Hasanov, Ivanov and Nedzhibov as well as recent work of McDaugall and Wotherspoon. For each method obtained in this thesis, the order of convergence has been calculated and compared with that of the similar existing methods. Also, most of the methods are supported by numerical examples.