Some iterative methods free from second derivatives for nonlinear equations

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

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

Two new three and four parametric with memory methods for solving nonlinear ‎equations

In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, Mathematical and Computer Modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...

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...

High order quadrature based iterative method for approximating the solution of nonlinear equations

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...