TITLE:
Steffensen-Type Method of Super Third-Order Convergence for Solving Nonlinear Equations
AUTHORS:
Zhongli Liu, Hong Zhang
KEYWORDS:
Newton’s Method, Steffensen’s Method, Derivative Free, Super-Cubic Convergence, Nonlinear Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.7,
June
13,
2014
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.