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 JAMP  Vol.2 No.7 , June 2014
Steffensen-Type Method of Super Third-Order Convergence for Solving Nonlinear Equations
Zhongli Liu, Hong Zhang
Abstract: In this paper, a one-step Steffensen-type method with super-cubic convergence for solving nonlinear equations is suggested. The convergence order 3.383 is proved theoretically and demonstrated numerically. This super-cubic convergence is obtained by self-accelerating second-order Steffensen’s method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Its theoretical results and high computational efficiency is confirmed by Numerical examples.
Keywords: Newton’s Method, Steffensen’s Method, Derivative Free, Super-Cubic Convergence, Nonlinear Equation
Cite this paper: Liu, Z. and Zhang, H. (2014) Steffensen-Type Method of Super Third-Order Convergence for Solving Nonlinear Equations. Journal of Applied Mathematics and Physics, 2, 581-586. doi: 10.4236/jamp.2014.27064.
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