On the development of Steffensen’s method and applications to Hammerstein equations

We construct an analog of Steffensen’s method for solving nonlinear operator equations. Proposed method is a kind of two stage iterative process. We study the order of convergence of the method. It is shown that the proposed analog of Stefensen’s method, which does not use derivatives, has higher order of convergency then Newton method, other generalizations of chord method or other known modifications of Steffensen’s method. Results of numerical experiments with Hammerstein equation are presented.