IJPAM: Volume 84, No. 5 (2013)
METHODS WITH EIGHTH-ORDER OF CONVERGENCE
FOR SOLVING NONLINEAR EQUATIONS
1,3Department of Mathematics
Faculty of Science
Almadinah Almanwarra, KINGDOM OF SAUDI ARABIA
2Al-Huson University College
Al-Balqa Applied University
Abstract. In this paper, a new one parameter family of iterative methods with eighth-order of convergence for solving nonlinear equations is presented and analyzed. This new family of iterative methods is obtained by composing an iterative method proposed by Chun  with Newton's method and approximating the first-appeared derivative in the last step by a combination of already evaluated function values. The proposed family is optimal since its efficiency index is 81/4 ≈ 1.6818. The convergence analysis of the new family is studied in this paper. Several numerical examples are presented to illustrate the efficiency and accuracy of the family.
Received: July 26, 2011
AMS Subject Classification: 41A25, 65H05
Key Words and Phrases: Newton's method, iterative methods, efficiency index, order of convergence, optimal eighth-order
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DOI: 10.12732/ijpam.v84i5.1 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395