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...

omotopy analysis method (ham) is a promising method for handling func-tional equations. recent publications proved the eectiveness of ham in solvingwide variety of problems in dierent elds. ham has a unique property whichmakes it superior to other analytic methods, this property is its ability to con-trol the convergence region of the solution series. in this work, we claried theadvantages ...

A class of derivative-free methods without memory for approximating a simple zero of a nonlinear equation is presented. The proposed class uses four function evaluations per iteration with convergence order eight. Therefore, it is an optimal three-step scheme without memory based on Kung-Traub conjecture. Moreover, the proposed class has an accelerator parameter with the property that it can in...