A new Householders method free from second derivatives for solving nonlinear equations and polynomiography

A modification of Chebyshev-Halley method free from second derivatives for nonlinear equations

‎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...

a modification of chebyshev-halley method free from second derivatives for nonlinear equations

‎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...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

Some iterative methods free from second derivatives for nonlinear equations

In a recent paper, Noor [M. Aslam Noor, New classes of iterative methods for nonlinear equations, Appl. Math. Comput., 2007, doi:10.1016/j.amc:2007], suggested and analyzed a generalized one parameter Halley method for solving nonlinear equations using. In this paper, we modified this method which has fourth order convergence. As special cases, we obtain a family of third-order iterative method...

New Efficient Optimal Derivative-Free Method for Solving Nonlinear Equations

In this paper, we suggest a new technique which uses Lagrange polynomials to get derivative-free iterative methods for solving nonlinear equations. With the use of the proposed technique and Steffens on-like methods, a new optimal fourth-order method is derived. By using three-degree Lagrange polynomials with other two-step methods which are efficient optimal methods, eighth-order methods can b...