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New Twelfth Order J-Halley Method for Solving Nonlinear Equations
Current Issue
Volume 1, 2013
Issue 1 (December)
Pages: 1-4   |   Vol. 1, No. 1, December 2013   |   Follow on         
Paper in PDF Downloads: 31   Since Aug. 28, 2015 Views: 1802   Since Aug. 28, 2015
Authors
[1]
Farooq Ahmad, Mathematics Department, College of Science, Majmaah University, Alzulfi, Saudi Arabia.
[2]
Sajjad Hussain, Mathematics Department, College of Science, Majmaah University, Alzulfi, Saudi Arabia.
[3]
Sifat Hussain, Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
[4]
Arif Rafiq, Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan.
Abstract
In a paper, Noor and Noor [Predictor--corrector Halley method for nonlinear equations, Appl. Math. Comput., 188 (2) (2007) 1587--1591] have suggested and analyzed a predictor--corrector method Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which has a quantic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method is a robust one. Several examples are given to illustrate the efficiency and the performance of this new method.
Keywords
Halley Method, Jarratt Method, Iterative Methods, Convergence Order, Numerical Examples
Reference
[1]
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M. A. Noor, Numerical Analysis and Optimization, Lecture Notes, Mathematics Department, COMSATS Institute of information Technology, Islamabad, Pakistan, 2006.
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M. A. Noor and K. I. Noor, Fifth-order iterative methods for solving nonlinear equations, Appl. Math. Comput. 188 (1) (2007) 406-410.
[12]
K. I. Noor and M. Aslam Noor, Predictor--corrector Halley method for nonlinear equations, Appl. Math. Comput., 188 (2) (2007) 1587--1591.
[13]
J. F. Traub, Iterative Methods for Solution of Equations, Prentice-Hall, Englewood, Cliffs, NJ, 1964.
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