There are a very small number of high quality derivative free methods with memory for
solving a system of nonlinear equations numerically. Motivated and inspired by the fact, we …

In this work, we first develop a new family of three-step seventh-and eighth-order Newton-
type iterative methods for solving systems of nonlinear equations. We also propose some …

In this manuscript, by using undetermined parameter method, an efficient iterative method
with eighth-order is designed to solve nonlinear systems. The new method requires one …

Two novel Kurchatov-type first-order divided difference operators were designed, which
were used for constructing the variable parameter of three derivative-free iterative methods …

Some Kurchatov-type accelerating parameters are used to construct some derivative-free
iterative methods with memory for solving nonlinear systems. New iterative methods are …

The application of fractional calculus for solving nonlinear equations through iterative
techniques is an emerging area of research. In recent times, several Newton-type methods …

Many applications from a wide variety of disciplines in the natural sciences and also in
engineering are reduced to solving of an equation or a system of equations in a …

In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear
systems is presented. The fourth-order convergence for all the elements of the class is …

Power flow problems can be solved in a variety of ways by using the Newton–Raphson
approach. The nonlinear power flow equations depend upon voltages V i and phase angle …

In this paper, we consider two-step fourth-order and three-step sixth-order derivative free
iterative methods and study their convergence in Banach spaces to approximate a locally …