In this paper, we present some new third-order iterative methods for finding a simple root α
of nonlinear scalar equation f (x)= 0 in R. A geometric approach based on the circle of …

The main motivation of this study is to present an optimal scheme in a general way that can
be applied to any existing optimal multipoint fourth-order iterative scheme whose first …

In this paper, we define a new wide class of iteration functions and then we use it to prove a
general convergence theorem that provides exact domain of initial approximations to …

Establishment of a new optimal higher-order iterative scheme for multiple zeros with known
multiplicity (m≥ 1) of univariate function is one of the hard and demanding task in the area …

We develop a new simple iteration formula, which does not require any derivatives of f (x),
for solving a nonlinear equation f (x)= 0. It is proved that the convergence order of the new …

We present another simple way of deriving several iterative methods for solving nonlinear
equations numerically. The presented approach of deriving these methods is based on …

In this paper, based on the basic principle of the SPH method's kernel approximation, a new
kernel approximation was constructed to compute first-order derivative through Taylor series …

In this paper, we propose a new cubically convergent family of super-Halley method based
on power means. Some well-known methods can be regarded as particular cases of the …

In this paper we propose a simple iterative method for finding a root of a nonlinear equation.
It is shown that the new method, which does not require any derivatives, has a quadratic …

Construction of two-point sixth-order methods for simple root is an ambitious and
challenging task in numerical analysis. Therefore, the main aim of this paper is to introduce …