Newton Type Iterative Methods for Solving Nonlinear Equations
Date
2017
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Mathematics
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.
Description
Keywords
Mathematics, Nonlinear equations, Iterative methods