A New Family of Nonlinear Fifth-Order Solvers for Finding Simple Roots

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References

[1] J. F. Traub, “Iterative Methods for the Solution of Equations,” Prentice Hall, Upper Saddle River, 1964.

[2] C. Chun, “Some Variants of King’s Fourth-Order Family of Methods for Nonlinear Equations,” Applied Mathematics and Computation, Vol. 190, No. 1, 2007, pp. 5762. doi:10.1016/j.amc.2007.01.006

[3] A. M. Ostrowski, “Solution of Equations in Euclidean and Banach Space,” Academic Press, New York, 1973.

[4] B. Ghanbari, “A New General Fourth-Order Family of Methods for Findingsimple Roots of Nonlinear Equations,” Journal of King Saud University—Science, Vol. 23, No. 1, 2011, pp. 395-398.

[5] L. Fang, L. Sun and G. He, “An Efficient Newton-Type Method with Fifth-Order Convergence for Solving Nonlinear Equations,” Computational Applied Mathematics, Vol. 27, No. 3, 2008, pp. 269-274.

[6] Y. M. Ham and C. Chun, “A Fifth-Order Iterative Method for Solving Nonlinear Equations,” Applied Mathematics and Computation, Vol. 194, No. 1, 2007, pp. 287-290.
doi:10.1016/j.amc.2007.04.005

[7] L. Fang and G. He, “Some Modifications of Newton’s Method with Higher-Order Convergence for Solving Nonlinear Equations,” Journal of Computational and Applied Mathematics, Vol. 228, No. 1, 2009, pp. 296-303.
doi:10.1016/j.cam.2008.09.023

[8] J. Biazar and B. Ghanbari, “Some Higher-Order Families of Methods for Finding Simple Roots of Nonlinear Equations,” General Mathematics Notes, Vol. 7, No. 1, 2011, pp. 46-51.

[9] W. Gautschi, “Numerical Analysis: An Introduction,” Birkh?user, Boston, 1997.

[10] M. Grau and J. L. Diaz-Barrero, “An Improvement of the Euler-Chebyshev Iterative Method,” Journal of Mathematical Analysis and Applications, Vol. 315, No. 1, 2006, pp. 1-7. doi:10.1016/j.jmaa.2005.09.086

[11] Y. M. Ham, C. Chun and S. Lee, “Some Higher-Order Modifications of Newton’s Method for Solving Nonlinear Equations,” Journal of Computational and Applied Mathematics, Vol. 222, No. 2, 2008, pp. 477-486.
doi:10.1016/j.cam.2007.11.018

[12] J. Kou and Y. Li, “The Improvements of ChebyshevHalley Methods with Fifth-Order Convergence,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 143-147. doi:10.1016/j.amc.2006.09.097