Author(s)

Quan Zheng, Xiuhui Guo, Fengxi Huang

College of Sciences, North China University of Technology, Beijing 100144, China.

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.

Nonlinear equation; Newton's method; Steffensen-type method; Derivative free; Super convergence

Zheng, Q. , Guo, X. and Huang, F. (2012) Self-accelerating two-step Steffensen-type methods with memory and their applications on the solution of nonlinear BVPs. Open Journal of Applied Sciences, 2, 70-73. doi: 10.4236/ojapps.2012.24B017.