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A new fourth-order family for solving nonlinear problems and its dynamics


In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made in order to choose those elements of the family with better conditions of stability. These results are checked by solving the nonlinear system that arises from the partial differential equation of molecular interaction.

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The authors thank to the anonymous referees for their suggestions to improve the paper.

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Correspondence to Juan R. Torregrosa.

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This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-\(\{01,02\}\) and Universitat Politècnica de València SP20120474.

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Cordero, A., Feng, L., Magreñán, A. et al. A new fourth-order family for solving nonlinear problems and its dynamics. J Math Chem 53, 893–910 (2015).

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  • Nonlinear systems
  • Iterative methods
  • Complex dynamics
  • Parameter space
  • Basins of attraction
  • Stability

Mathematics Subject Classfication

  • 65H05