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Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Volume
275
Identifiers
DOI: 10.1016/j.cam.2014.06.010
Keywords
  • Nonlinear Systems
  • Iterative Methods
  • Convergence Order
  • Computational Cost
  • Efficiency
  • Dynamics
Disciplines
  • Computer Science

Abstract

Abstract In this work we present a new family of iterative methods for solving nonlinear systems that are optimal in the sense of Kung and Traub’s conjecture for the unidimensional case. We generalize this family by performing a new step in the iterative method, getting a new family with order of convergence six. We study the efficiency of these families for the multidimensional case by introducing a new term in the computational cost defined by Grau-Sánchez et al. A comparison with already known methods is done by studying the dynamics of these methods in an example system.

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