Efficient Family of Iterative Methods for Solving Nonlinear Simultaneous Equations: A Comparative Study

Abstract

The solution of a system of nonlinear equations is presumably one of the most common but difficult features in numerical analysis in the sense of different aspirations for instance; high accuracy, minimum computation time, a small number of iterations along with less computational cost. In this study, four distinct iterative methods are presented for solving a system of nonlinear equations such as Broyden's method (BM), Optimal fourth-order method (OFOM), Optimal sixth order method (OSOM), and Homotopy continuation method (HCM). Detail formulations are explained along with the solution procedure. In addition, the rate of convergence and computational complexities are also explained within the formulations. Furthermore, to demonstrate and compare the efficiency of these methods, we solve two real-world practical nonlinear models. However, the results are presented numerically in a tabular form and the approximate results are compared with the exact and approximate solutions of other existing iterative methods. After analyzing the results, we conclude which method is better in what aspects.