Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 3, June 2017, Pages: 106-109
Received: Apr. 11, 2017; Accepted: Apr. 21, 2017; Published: May 19, 2017
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Authors
Ahmad Syakir, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
M. Imran, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Moh Danil Hendry Gamal, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
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Abstract
This article discusses the modification of three step iteration method to solve nonlinear equations f (x)=0. The new iterative method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, some derivatives in this method are estimated by Taylor polynomials. Using analysis of convergence we show that the new method has the order of convergence fourteen. Numerical computation shows that the new method are comparable to other methods discussed.
Keywords
Free Second Derivative Method, Taylor Series, Iterative Method, Order of Convergence
To cite this article
Ahmad Syakir, M. Imran, Moh Danil Hendry Gamal, Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives, International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 3, 2017, pp. 106-109. doi: 10.11648/j.ijtam.20170303.12
Copyright
Copyright © 2017 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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