CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems

  • Francisco I. ChicharroEmail author
  • Alicia Cordero
  • Tobías H. Martínez
  • Juan R. Torregrosa
Original Paper


The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods have been proposed in the literature. The evolution of these methods in terms of order of convergence implies the inclusion of a weight function for each case, showing an optimal fourth-order convergence, in the sense of Kung–Traub’s conjecture. The analysis of these new schemes is performed by means of complex dynamics. These methods are applied on the solution of the nonlinear Colebrook–White equation and the nonlinear system of the equilibrium conversion, both frequently used in Chemistry.


Nonlinear systems Iterative method Weight functions Complex dynamics Basin of attraction Chemical applications 

Mathematics Subject Classification

MSC 65H05 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Escuela Superior de Ingeniería y TecnologíaUniversidad Internacional de La RiojaLogroñoSpain
  2. 2.Institute for Multidisciplinary MathematicsUniversitat Politècnica de ValènciaValènciaSpain

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