Low-complexity root-finding iteration functions with no derivatives of any order of convergence

摘要

In this paper, a procedure to design Steffensen-type methods of different orders for solving nonlinear equations is suggested. By using a particular divided difference of first order we can transform many iterative methods into derivative-free iterative schemes, holding the order of convergence of the departure original method. Numerical examples and the study of the dynamics are made to show the performance of the presented schemes and to compare them with another ones.