Open AccessVarious Newton-type iterative methods for solving nonlinear equations
Author(s) -
Manoj Kumar,
Akhilesh Kumar Singh,
Akanksha Srivastava
Publication year - 2013
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.03.001
Subject(s) - local convergence , newton's method , newton's method in optimization , iterative method , mathematics , steffensen's method , convergence (economics) , nonlinear system , matlab , type (biology) , derivative (finance) , ninth , mathematical optimization , computer science , economics , biology , economic growth , ecology , physics , quantum mechanics , financial economics , acoustics , operating system
The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods