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Authors: Wang, Xiaofeng | Zhang, Tie

Article Type: Research Article

Abstract: Based on Petković-Ilić-Džunić method [3], we derive a family of three-step eighth-order Steffensen type iterative methods for solving nonlinear equations. The new methods without memory use two suitable parametric functions at the second and third steps and are free from any derivatives. Per iteration the new methods require four functional evaluations, which implies that the efficiency index of the new methods is 1.682. The advantage of the new methods is that the computing speed of the new methods is faster than that of other eighth-order Steffensen type methods without memory. Numerical examples are made to show the performance of our …methods and support the developed theory. Show more

Keywords: Steffensen method, Newton method, derivative free, eighth-order convergence, root-finding

DOI: 10.3233/JCM-140505

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 14, no. 4-5, pp. 277-287, 2014

Authors: Wang, Xiao-Feng | Zhang, Tie | Zheng, Fu | Qian, Wei-Yi

Article Type: Research Article

Abstract: In this paper, we present a new iterative method of convergence order five for solving nonlinear systems. Per iteration the new method requires the evaluations of two functions, two first derivatives and one matrix inversion. The computational efficiency index is used to compare the efficiency of different methods. Numerical tests are performed, which confirm the theoretical results. From the comparison with the existing methods it is observed that the new method is more efficient in both computational efficiency and computational time.

Keywords: Iterative method, Newton's method, nonlinear systems, computational efficiency

DOI: 10.3233/JCM-140512

Citation: Journal of Computational Methods in Sciences and Engineering, vol. 14, no. 6, pp. 363-372, 2014