Extended Kurchatov-type methods for solving nonlinear equations

A plethora of applications from diverse disciplines can be solved if reduced to nonlinear equations in suitable abstract spaces. Such equations are solved mostly iteratively. That is why, three-step iterative methods of the Kurchatov-type for solving nonlinear operator equations are investigated using approximation by the Frechet derivative of an operator of a nonlinear equation by divided di erences. We study the local and the semi-local convergence using conditions only on the operators on the methods. The conditions and speed of convergence of these methods are determined. Moreover, the domain of uniqueness is found for the solution. The results of numerical experiments validate the theoretical results. The new idea can be used on other iterative methods utilizing inverses of divided di erences of order one.