Steffensen-Type Method of Super Third-Order Convergence for Solving Nonlinear Equations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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