Nonlinear equations are frequently encountered in many areas of applied science and
engineering, and they require efficient numerical methods to solve. To ensure quick and …

A straightforward family of one-point multiple-root iterative methods is introduced. The family
is generated using the technique of weight functions. The order of convergence of the family …

In this paper, we describe iterative derivative-free algorithms for multiple roots of a nonlinear
equation. Many researchers have evaluated the multiple roots of a nonlinear equation using …

In this manuscript, we present a new general family of optimal iterative methods for finding
multiple roots of nonlinear equations with known multiplicity using weight functions. An …

A number of higher order Newton-like methods (ie the methods requiring both function and
derivative evaluations) are available in literature for multiple zeros of a nonlinear function …

We present a new family of optimal eighth-order numerical methods for finding the multiple
zeros of nonlinear functions. The methodology used for constructing the iterative scheme is …

In this manuscript, we introduce a higher‐order optimal family of Chebyshev–Halley type
methods to solve a univariate nonlinear equation having multiple roots. The proposed …

Many practical problems, such as the Malthusian population growth model, eigenvalue
computations for matrices, and solving the Van der Waals' ideal gas equation, inherently …

We present a new iterative procedure for solving nonlinear equations with multiple roots with
high efficiency. Starting from the arithmetic mean of Newton's and Chebysev's methods, we …

In the study of systems' dynamics the presence of symmetry dramatically reduces the
complexity, while in chemistry, symmetry plays a central role in the analysis of the structure …