In this paper, we present some new variants of Chebyshev-Halley methods free from second derivative for solving nonlinear equation of the type f(x) = 0, and show that the convergence orders of the proposed methods are three or four. Several numerical examples are given to illustrate the efficiency and performance of the new methods.

In this article, we have combined two well known third order methods one is Chebyshev and another Super- Halley to form an iterative method of for solving polynomial equations with multiple zeros. This constructed basically the mean Super-Halley, so name as C-S Combined Mean Method. We proposed some local convergence theorems Method establish computation a For establishment theorem, key role pe...

This paper is dedicated to the study of continuous Newton’s method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerical methods for solving initial value problems. The relationship between the step size and the order of ...

In this paper, a complex dynamical study of a parametric Chebyshev-Halley type family of iterative methods on quadratic polynomial is presented. The stability of the fixed points is analyzed in terms of the parameter of the family. We also calculate the critical points building their corresponding parameter planes which allow us to analyze the qualitative behaviour of this family. Moreover, we ...

It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian (Df(x) · d) can be calculated at a cost proportional to that of a state-of-the-art method for calculating the Hessian matrix. We do this by first presenting a simple procedure for designing high order reverse methods and applying it t...

‎In this paper‎, ‎we present a new modification of Chebyshev-Halley‎ ‎method‎, ‎free from second derivatives‎, ‎to solve nonlinear equations‎. ‎The convergence analysis shows that our modification is third-order‎ ‎convergent‎. ‎Every iteration of this method requires one function and‎ ‎two first derivative evaluations‎. ‎So‎, ‎its efficiency index is‎ ‎$3^{1/3}=1.442$ that is better than that o...