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.
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