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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 957496, 8 pages
Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations
1Petroleum Engineering Department, UNISTMO, 70760 Tehuantepec, OAX, Mexico
2Applied Mathematics Department, UNISTMO, 70760 Tehuantepec, OAX, Mexico
Received 21 November 2012; Revised 24 January 2013; Accepted 2 February 2013
Academic Editor: Michael Ng
Copyright © 2013 Gustavo Fernández-Torres and Juan Vásquez-Aquino. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. A. Noor and W. A. Khan, “Fourth-order iterative method free from second derivative for solving nonlinear equations,” Applied Mathematical Sciences, vol. 6, no. 93–96, pp. 4617–4625, 2012.
- A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “New modifications of Potra-Pták's method with optimal fourth and eighth orders of convergence,” Journal of Computational and Applied Mathematics, vol. 234, no. 10, pp. 2969–2976, 2010.
- C. Chun, “A geometric construction of iterative formulas of order three,” Applied Mathematics Letters, vol. 23, no. 5, pp. 512–516, 2010.
- Z. Li, C. Peng, T. Zhou, and J. Gao, “A new Newton-type method for solving nonlinear equations with any integer order of convergence,” Journal of Computational Information Systems, vol. 7, no. 7, pp. 2371–2378, 2011.
- H. T. Kung and J. F. Traub, “Optimal order of one-point and multipoint iteration,” Journal of the Association for Computing Machinery, vol. 21, pp. 643–651, 1974.
- A. M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, NY, USA, 1966.
- A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis, McGraw-Hill, 1978.
- E. Halley, “A new, exact and easy method of finding the roots of equations generally and that without any previous reduction,” Philosophical Transactions of the Royal Society of London, vol. 18, pp. 136–148, 1964.
- E. Hansen and M. Patrick, “A family of root finding methods,” Numerische Mathematik, vol. 27, no. 3, pp. 257–269, 1977.
- N. Osada, “An optimal multiple root-finding method of order three,” Journal of Computational and Applied Mathematics, vol. 51, no. 1, pp. 131–133, 1994.
- H. D. Victory and B. Neta, “A higher order method for multiple zeros of nonlinear functions,” International Journal of Computer Mathematics, vol. 12, no. 3-4, pp. 329–335, 1983.
- R. F. King, “A family of fourth order methods for nonlinear equations,” SIAM Journal on Numerical Analysis, vol. 10, pp. 876–879, 1973.
- C. Chun and B. Neta, “A third-order modification of Newton's method for multiple roots,” Applied Mathematics and Computation, vol. 211, no. 2, pp. 474–479, 2009.
- A. Cordero and J. R. Torregrosa, “A class of Steffensen type methods with optimal order of convergence,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7653–7659, 2011.
- Q. Zheng, J. Li, and F. Huang, “An optimal Steffensen-type family for solving nonlinear equations,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9592–9597, 2011.
- M. S. Petković, J. Džunić, and B. Neta, “Interpolatory multipoint methods with memory for solving nonlinear equations,” Applied Mathematics and Computation, vol. 218, no. 6, pp. 2533–2541, 2011.
- J. Džunić, M. S. Petković, and L. D. Petković, “Three-point methods with and without memory for solving nonlinear equations,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 4917–4927, 2012.