Self-accelerating two-step Steffensen-type methods with memory and their applications on the solution of nonlinear BVPs

Quan Zheng, Xiuhui Guo, Fengxi Huang

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

DOI: 10.4236/ojapps.2012.24B017                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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