New technique for the approximation of the zeros of nonlinear scientific models

Abstract

Most of the problems in mathematical and engineering sciences can be studied in the context of nonlinear equations. In this paper, we develop a new family of iterative methods for the approximation of the zeros of mathematical models whose governing equations are nonlinear in nature. The proposed methods are based on decomposition technique due to Daftardar-Gejji and Jaffri [1]. The new family gives several iterative schemes as special cases. The convergence analysis of proposed methods is also presented. In order to determine the performance of newly developed methods, numerical as well as graphical analysis of four complex mathematical models from diverse fields of science and engineering are considered. We also consider some complex polynomials to visualize the roots through polynomiography in the context of proposed methods.

An optimal fourth-order second derivative free iterative method for nonlinear scientific equations

“…Acording to this conjecture, an iterative method is said to be an optimal one if it needs (n + 1) evaluations per iteration and posses convergence order 2 n . Some useful optimal fourth-order iterative methods have been constructed by various researchers (Sharma et al, 2020;Ali et al, 2020;Shams et al, 2020;Cordero et al, 2021;Hafiz and Khirallah, 2021). Cordero et al, (2010) introduced the following optimal fourth-order method:…”