New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations
American Journal of Applied Mathematics
Volume 4, Issue 4, August 2016, Pages: 175-180
Received: May 16, 2016; Accepted: May 31, 2016; Published: Jun. 17, 2016
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Author
Noori Yasir Abdul-Hassan, Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq
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Abstract
In this paper, we propose and analyze new two efficient iterative methods for finding the simple roots of nonlinear equations. These methods based on a Jarratt's method, Householder's method and Chun&Kim's method by using a predictor-corrector technique. The error equations are given theoretically to show that the proposed methods have twelfth-order convergence. Several numerical examples are given to illustrate the efficiency and robustness of the proposed methods. Comparison with other well-known iterative methods is made.
Keywords
Nonlinear Equations, Predictor-Corrector Methods, Convergence Analysis, Efficiency Index, Numerical Examples
To cite this article
Noori Yasir Abdul-Hassan, New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations, American Journal of Applied Mathematics. Vol. 4, No. 4, 2016, pp. 175-180. doi: 10.11648/j.ajam.20160404.12
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Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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