A composite third order Newton–Steffensen method for solving nonlinear equations

摘要

In this paper, we suggest a third-order method formed by the composition of Newton and Steffensen methods for finding simple and real roots of a nonlinear equation in single variable. Per iteration the formula requires two evaluations of the function and single evaluation of the derivative. Experiments show that the method is suitable in the cases where Newton and Steffensen methods fail.