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Stability analysis of fourth-order iterative method for finding multiple roots of non-linear equations

Authors
  • Cordero, Alicia1
  • Jaiswal, Jai P.2
  • Torregrosa, Juan R.1
  • 1 Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Cno. de Vera s/n, 46022 , (Spain)
  • 2 Department of Mathematics, Maulana Azad National Institute of Technology, M.P.-462051 , (India)
Type
Published Article
Journal
Applied Mathematics and Nonlinear Sciences
Publisher
Sciendo
Publication Date
Apr 19, 2019
Volume
4
Issue
1
Pages
43–56
Identifiers
DOI: 10.2478/AMNS.2019.1.00005
Source
De Gruyter
Keywords
License
Green

Abstract

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 in the last few years with fruitful results. Most of the studies dealt with the analysis of iterative schemes for solving non-linear equations with simple roots; however, the case involving multiple roots remains almost unexplored. The main objective of this paper was to discuss the dynamical analysis of the rational map associated with an existing class of iterative procedures for multiple roots. This study was performed for cases of double and triple multiplicities, giving as a conjecture that the wideness of the convergence regions of the multiple roots increases when the multiplicity is higher and also that this family of parametric methods includes some specially fast and stable elements with global convergence.

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