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

Ramandeep Behl, Alicia Cordero, S.S. Motsa and Juan R. Torregrosa

Applied Mathematics and Computation, 2015, vol. 265, issue C, 520-532

Abstract: 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 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.

Keywords: Nonlinear equations; Multiple roots; Halley’s method; Schröder method; Complex dynamics; Basin of attraction (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:520-532

DOI: 10.1016/j.amc.2015.05.004

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