TITLE:
Self-accelerating two-step Steffensen-type methods with memory and their applications on the solution of nonlinear BVPs
AUTHORS:
Quan Zheng, Xiuhui Guo, Fengxi Huang
KEYWORDS:
Nonlinear equation; Newton's method; Steffensen-type method; Derivative free; Super convergence
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.2 No.4B,
January
14,
2013
ABSTRACT: In this paper, seven self-accelerating iterative
methods with memory are derived from an optimal two-step Steffensen-type method
without memory for solving nonlinear equations, their orders of convergence are
proved to be increased,numerical examples are demonstrat-ed demonstrated to verify the theoretical results, and applications for solving systems of
nonlinear equations and BVPs of nonlinear ODEs are illustrated.