IJPAM: Volume 93, No. 1 (2014)

THREE-STEP ITERATIVE METHOD WITH
EIGHTEENTH ORDER CONVERGENCE FOR
SOLVING NONLINEAR EQUATIONS

Mohamed S.M. Bahgat$^1$, M.A. Hafiz$^2$
$^1$Department of Mathematics
Faculty of Science
El-Minia University
EGYPT
$^{1,2}$Department of Mathematics
Faculty of Science and Arts
Najran University
Najran, 1988, SAUDI ARABIA


Abstract. In this paper, we propose and discuss a new higher-order iterative method for solving nonlinear equations. This method based on a Halley and Householder iterative method and using predictor-corrector technique. The convergence analysis of our method is discussed. It is established that the new method has convergence order eighteen. Numerical tests show that the new method is comparable with the well-known existing methods and gives better results.

Received: November 9, 2013

AMS Subject Classification: 41A25, 65H05, 65K05

Key Words and Phrases: nonlinear equations, convergence analysis, higher order convergence, iterative method

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DOI: 10.12732/ijpam.v93i1.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 1
Pages: 85 - 94

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).