In this paper, we propose two novel iteration schemes for computing zeros of nonlinear
equations in one dimension. We develop these iteration schemes with the help of Taylor's …

In this study, we present a new higher-order scheme without memory for simple zeros which
has two major advantages. The first one is that each member of our scheme is derivative …

In this article, we propose some novel computational methods in the form of iteration
schemes for computing the roots of non-linear scalar equations in a new way. The …

In this study, we construct the one parameter optimal derivative-free iterative family to find
the multiple roots of an algebraic nonlinear function. Many researchers developed the …

Two new efficient families of multipoint iterative methods of fourth and eighth order
convergence are constructed for finding simple roots of nonlinear equation Γ (s)= 0. Both …

To locate a locally-unique solution of a nonlinear equation, the local convergence analysis
of a derivative-free fifth order method is studied in Banach space. This approach provides …

In this article, we design a novel fourth‐order and derivative free root‐finding algorithm. We
construct this algorithm by applying the finite difference scheme on the well‐known …

Finding higher-order optimal derivative-free methods for multiple roots (m≥ 2) of nonlinear
expressions is one of the most fascinating and difficult problems in the area of numerical …

Here, we suggest a high-order optimal variant/modification of Schröder's method for
obtaining the multiple zeros of nonlinear uni-variate functions. Based on quadratically …

In this paper, some iterative methods with third order convergence for solving the nonlinear
equation were reviewed and analyzed. The purpose is to find the best iteration schemes that …