SOME NEW DERIVATIVE FREE METHODS FOR SOLVING NONLINEAR EQUATIONS

This paper proposes two new iterative methods for solving nonlinear equations. In comparison to the classical Newton’s method, the new proposed methods do not use derivatives; furthermore only two evaluations of the function are needed per iteration. Using the methods proposed, when the starting value is selected close to the root, the order of convergence is 2. The development of the method allows you to achieve classical methods such as secant and Steffensen’s as an alternative to the usual process. The numerical examples show that the proposed methods have the same performance as Newton’s method with the advantage of being derivative free. In comparison to other methods which are derivative free, these methods are more efficient.