On developing fourth-order optimal families of methods for multiple roots and their dynamics

Abstract

[EN] There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity in of the required loot is known in advance. Therefore, the first focus of this paper is on developing new fourth order optimal families of iterative methods by a simple and elegant way. Computational and theoretical properties are fully studied along with a main theorem describing the convergence analysis. Another main focus of this paper is the dynamical analysis of the rational map associated with our proposed class for multiple roots; as far as we know, there are no deep study of this kind on iterative methods for multiple roots. Further, using Mathematica with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm the theoretical development. (C) 2015 Elsevier Inc. All rights reserved.