Dynamical Analysis of an Optimal Iterative Scheme and its Real-Life Applications.

The weight function approach of solving nonlinear equations is presented in this work as a two-step, fourth-order, optimal iterative method. It comes from the idea of the theoretical order of convergence. The performance of the novel method has been assessed on a small number of real-life applications from different domains and contrasted with the fourth-order methods currently in use. Also, we find that this has fewer errors and iterations for the same order than the methods now in use. To examine the dynamical analysis of the proposed method using computer tools, we test some challenging polynomials that explain convergence and other graphical features of the iterative scheme. [ABSTRACT FROM AUTHOR]