• A new efficient parametric family of iterative methods for solving nonlinear systems 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Journal of Difference Equations and Applications, 18/09/2019)
      A bi-parametric family of iterative schemes for solving nonlinear systems is presented. We prove for any value of parameters the sixth-order of convergence of any members of the class. The efficiency and computational ...
    • A new fourth-order family for solving nonlinear problems and its dynamics 

      Cordero, Alicia; Feng, Licheng; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 03/2015)
      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 ...
    • CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Martínez, Tobias H. (1); Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 03/2020)
      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 ...
    • Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (MDPIMathematics, 05/12/2019)
      A generalized high-order class for approximating the solution of nonlinear systems of equations is introduced. First, from a fourth-order iterative family for solving nonlinear equations, we propose an extension to nonlinear ...
    • Highly efficient family of iterative methods for solving nonlinear models 

      Behl, Ramandeep; Sarría, Íñigo (1); González-Crespo, Rubén (1); Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 15/01/2019)
      In this study, we present a new highly efficient sixth-order family of iterative methods for solving nonlinear equations along with convergence properties. Further, we extend this family to the multidimensional case ...
    • On the improvement of the order of convergence of iterative methods for solving nonlinear systems by means of memory 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus (1); Torregrosa, Juan Ramón (Applied Mathematics Letters, 06/2020)
      Iterative methods with memory for solving nonlinear systems have been designed. For approximating the accelerating parameters the Kurchatov's divided difference is used as an approximation of the derivative of second order. ...