Table of Contents
International Journal of Engineering Mathematics
Volume 2016, Article ID 6390367, 18 pages
http://dx.doi.org/10.1155/2016/6390367
Research Article

A New Accurate and Efficient Iterative Numerical Method for Solving the Scalar and Vector Nonlinear Equations: Approach Based on Geometric Considerations

Aix-Marseille Université, IFSTTAR, LBA UMR T24, 13016 Marseille, France

Received 31 March 2016; Accepted 12 June 2016

Academic Editor: Josè A. Tenereiro Machado

Copyright © 2016 Grégory Antoni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with a new numerical iterative method for finding the approximate solutions associated with both scalar and vector nonlinear equations. The iterative method proposed here is an extended version of the numerical procedure originally developed in previous works. The present study proposes to show that this new root-finding algorithm combined with a stationary-type iterative method (e.g., Gauss-Seidel or Jacobi) is able to provide a longer accurate solution than classical Newton-Raphson method. A numerical analysis of the developed iterative method is addressed and discussed on some specific equations and systems.