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Journal of Mathematical Chemistry

, Volume 55, Issue 7, pp 1461–1480 | Cite as

Multidimensional stability analysis of a family of biparametric iterative methods: CMMSE2016

  • Alicia Cordero
  • Javier G. MaimóEmail author
  • Juan R. Torregrosa
  • María P. Vassileva
Original Paper

Abstract

In this paper, we present a multidimensional real dynamical study of the Ostrowsky–Chun family of iterative methods to solve systems of nonlinear equations. This family was defined initially for solving scalar equations but, in general, scalar methods can be transferred to make them suitable to solve nonlinear systems. The complex dynamical behavior of the rational operator associated to a scalar method applied to low-degree polynomials has shown to be an efficient tool for analyzing the stability and reliability of the methods. However, a good scalar dynamical behavior does not guarantee a good one in multidimensional case. We found different real intervals where both parameters can be defined assuring a completely stable performance and also other regions where it is dangerous to select any of the parameters, as undesirable behavior as attracting elements that are not solution of the problem to be solved appear. This performance is checked on a problem of chemical wave propagation, Fisher’s equation, where the difference in numerical results provided by those elements of the class with good stability properties and those showed to be unstable, is clear.

Keywords

Nonlinear system of equations Iterative method Basin of attraction Dynamical plane Stability Fisher’s equation 

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Alicia Cordero
    • 1
  • Javier G. Maimó
    • 2
    Email author
  • Juan R. Torregrosa
    • 1
  • María P. Vassileva
    • 2
  1. 1.Instituto de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Instituto Tecnológico de Santo Domingo (INTEC)Santo DomingoDominican Republic

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