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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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
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.
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.
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.
K. E. Atkinson, Elementary Numerical Analysis, third Ed., John Wiley & Sons, Inc., New York, 1993.
M. S. M. Bahgat and M. A. Hafiz, Three step iterative method with eighteenth order convergence for solving nonlinear equations, International Journal of Pure and Applied Mathematics, 93 (2014), 85-94.
R. Behl and V. Kanwar, Variant of Chebyshev's methods with optimal order convergence, Tamsui Oxford Journal of Information and Mathematical Sciences, 29 (2013), 39-53.
M. A. Hafiz, An efficient three step tenth order method without second order derivative, Palestine Journal of Mathematics, 3 (2014), 198-203.
M. A. Hafiz and S. M. H. Al-Goria, New ninth and seventh order methods for solving nonlinear equations, Europian Scientific Journal, 8 (2012), 83-95.
R. King, A family of fourth order methods for nonlinear equations, Journal of Numerical Analysis, 10 (1973), 876-879.
J. Kou, Y. Li, and X. Wang, Modified Halley's method free from second derivative, Applied Mathematics and Computation, 183 (2006), 704-708.
J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, third Ed., Prentice Hall, New Jersey, 1999.
M. Matinfar, M. Aminzadeh, and S. Asadpour, A new three step iterative method for solving nonlinear equations, Journal of Mathematical Extension, 6 (2012), 29-39.
K. I. Noor and M. A. Noor, Predictor-corrector Halley method for nonlinear equations, Applied Mathematics and Computation, 188 (2007), 1587-1591.
M. A. Noor, W. A. Khan, and A. Hussain, A new modified Halley method without second derivatives for nonlinear equations, Applied Mathematics and Computation, 189 (2007), 1268-1273.
M. Rafiullah and M. Haleem, Three step iterative method with sixth order convergence for solving nonlinear equations, International Journal of Mathematic Analysis, 50 (2010), 2459-2463.
G. Zavalani, A modification of Newton method with third order convergence, American Journal of Numerical Analysis, 2 (2014), 98-101.