Derivative-Free Iterative Methods for Solving Nonlinear Equations

Abstract

Abstract:In this paper, we suggest and analyze some new derivative free iterative methods for solving nonlinear equation f (x) = 0 using a suitable transformation. We also give several examples to illustrate the efficiency of these methods. Comparison with other similar method is also given. These new methods can be considered as alternative to the developed methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations.

Comparison of Proposed and Existing Fourth Order Schemes for Solving Non-linear Equations

“…Determining the root of a nonlinear equation is very important; researchers have developed numerical methods by involving derivatives [1]. Many algorithms have been introduced to accelerate the convergence of numerical methods without involving derivative [2,3,4,5,6,7]. By using covenant and suitable selection of parameters to reduce the number of evaluation of numerical method [2,8,9,6].…”

On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously

“…and * [2]. For a simple root ζ and small enough , |r (t) i - * s (t) j | is bounded away from zero, and so…”

“…Later, Farooq et al [2] presented the following derivative-free method having local quadratic convergence:…”

Advancing Nonlinear Problem Solutions: Newton-Like Iterative Techniques for Varied Convergence Orders using Homotopy Perturbation

“…al [6]. Many other researchers developed higher order derivative free iterative methods, see for example [7][8][9][10][11][12][13][14][15][16].…”