A new derivative-free method for solving nonlinear equations

Abstract

This paper presents a new method for solving nonlinear equations. The method is derivative-free and its convergence is linear. However, as numerical experiments conducted indicate, although its convergence is of order one, for certain problems, the method converges faster than some Newton-based methods of higher order; in particular, when Newton-based methods fail to converge, the method can be used to find the solution of the problem. Numerical experiments conducted also show that the method compares well with other iterative methods that do not depend on derivatives.