On an iterative Moser-Kurchatov method for solving systems of nonlinear equations

This paper is devoted to analysis of an iterative method for solving nonlinear equations. The method, inspired by the Kurchatov-type methods, is specifically designed to avoid the need for derivative calculations or inverses of linear operators. By employing a sequence of approximating operators and divided differences, the method achieves semilocal convergence. Numerical experiments demonstrate the method’s efficiency and robustness, highlighting its potential advantages over traditional methods like Newton’s method, especially in scenarios where derivative calculations are impractical and computationally expensive. The results indicate that the method is a viable and efficient alternative for solving nonlinear equations, especially in large-scale problems or scenarios, where derivative information is not readily available. The robustness and efficiency of the method make it a valuable tool in various scientific and engineering applications.