A plethora of higher order iterative methods, involving derivatives in algorithms, are
available in the literature for finding multiple roots. Contrary to this fact, the higher order …

The use of complex dynamics tools in order to deepen the knowledge of qualitative
behaviour of iterative methods for solving non-linear equations is a growing area of research …

Many optimal order multiple root techniques involving derivatives have been proposed in
literature. On the contrary, optimal order multiple root techniques without derivatives are …

There are few optimal fourth-order methods for solving nonlinear equations when the
multiplicity m of the required root is known in advance. Therefore, the first focus of this paper …

A number of optimal order multiple root techniques that require derivative evaluations in the
formulas have been proposed in literature. However, derivative-free optimal techniques for …

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–
Halley's iterative technique to solve the nonlinear equation having the multiple roots. The …

We suggest a derivative-free optimal method of second order which is a new version of a
modification of Newton's method for achieving the multiple zeros of nonlinear single variable …

Targeting a new multiple zero finder, in this paper, we suggest an efficient two-point class of
methods, when the multiplicity of the root is known. The theoretical aspects are investigated …

We construct an optimal eighth-order scheme which will work for multiple zeros with
multiplicity (m≥ 1), for the first time. Earlier, the maximum convergence order of multi-point …

In this paper, we propose a family of optimal eighth order convergent iterative methods for
multiple roots with known multiplicity with the introduction of two free parameters and three …