A nonstationary iterative second-order method for solving nonlinear equations

This paper presents a new nonstationary iterative method of second order for solving nonlinear equations, that does not require the use of any derivatives. For algebraic equations our method coincides with Newton's method, from a certain step of iteration on. Due to the methodology of Ostrowski [8], the efficiency index of our process equals 2, which is higher than the efficiency indices of classical iterative methods, such as Newton's process and the secant method, to mention just a few.