On some cubic convergence iterative formulae without derivatives for solving nonlinear equations

摘要

Finding the zeros of nonlinear functions has wide applications in engineering, in scientific computations and various other fields. In these problems we seek methods that lead to approximate solutions. Sometimes the applications of the iterative methods depending on the derivatives are restricted in engineering. In this paper, we propose some iterative formulae without derivatives. The convergence analysis shows that these methods are cubically convergent. The best property of these schemes is that they are derivative free. Several numerical examples are given to illustrate the efficiency and performance of the proposed methods.