A cubically convergent Steffensen-like method for solving nonlinear equations

A derivative free method for solving nonlinear equations of Steffensen’s type is presented. Using a self-correcting parameter, calculated by using Newton’s interpolatory polynomial of second degree, the R -order of convergence is increased from 2 to 3. This acceleration of the convergence rate is attained without any additional function calculations, which provides a very high computational efficiency of the proposed method. Another advantage is the convenient fact that this method does not use derivatives. Numerical examples are included to confirm the theoretical results and high computational efficiency.