This paper introduced a new iterative method for solving nonlinear equations using the derivative estimation technique for the third-order Taylor’s approximation. A comparative analysis of the new iterative technique to existing methods that can also be derived from Taylor’s approximation, such as Newton’s method (NM), Halley’s method (HM), and Gemechu’s method (GM), is also provided. A few examples of nonlinear equations have been solved where the results presented that the new iterative method has fourth-order convergence and is more accurate as compared to the previous methods.
