A family of hybrid derivative-free methods via acceleration parameter for solving system of nonlinear equations

A Family of Optimal Derivative Free Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations

In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimal three-step methods with eight-order convergence for solving the simple roots of nonlinear equations by using the weight function and interpolation methods. Per iteration this method requires four evaluations of the function which implies that the efficiency index of the d...

New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations

A new family of eighth-order derivative-freemethods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured...

Nonmonotone derivative-free methods for nonlinear equations

In this paper we study nonmonotone globalization techniques, in connection with iterative derivative-free methods for solving a system of nonlinear equations in several variables. First we define and analyze a class of nonmonotone derivative-free linesearch techniques for uncon-strained minimization of differentiable functions. Then we introduce a globalization scheme, which combines nonmonoton...

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

Comparison of acceleration techniques of analytical methods for solving differential equations of integer and fractional order

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.