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

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.