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Journal of Mathematical Chemistry

, Volume 56, Issue 7, pp 1902–1923 | Cite as

CMMSE2017: On two classes of fourth- and seventh-order vectorial methods with stable behavior

  • Alicia CorderoEmail author
  • Lucía Guasp
  • Juan R. Torregrosa
Original Paper

Abstract

A family of fourth-order iterative methods without memory, for solving nonlinear systems, and its seventh-order extension, are analyzed. By using complex dynamics tools, their stability and reliability are studied by means of the properties of the rational function obtained when they are applied on quadratic polynomials. The stability of their fixed points, in terms of the value of the parameter, its critical points and their associated parameter planes, etc. give us important information about which members of the family have good properties of stability and whether in any of them appear chaos in the iterative process. The conclusions obtained in this dynamical analysis are used in the numerical section, where an academical problem and also the chemical problem of predicting the diffusion and reaction in a porous catalyst pellet are solved.

Keywords

Nonlinear system of equations Iterative method Dynamical and Parameter planes Stability 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Instituto de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValenciaSpain

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