Dynamics and Stability on a Family of Optimal Fourth-Order Iterative Methods
Alicia Cordero,
Miguel A. Leonardo Sepúlveda,
Juan R. Torregrosa
Affiliations
Alicia Cordero
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
Miguel A. Leonardo Sepúlveda
Ciencias Básicas y Ambientales (CBA), Instituto Tecnológico de Santo Domingo (INTEC), Area de Ciencia Básica y Ambiental, Av. Los Próceres, Gala, Apartado Postal 342-9 and 249-2, Santo Domingo 10602, Dominican Republic
Juan R. Torregrosa
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
In this manuscript, we propose a parametric family of iterative methods of fourth-order convergence, and the stability of the class is studied through the use of tools of complex dynamics. We obtain the fixed and critical points of the rational operator associated with the family. A stability analysis of the fixed points allows us to find sets of values of the parameter for which the behavior of the corresponding method is stable or unstable; therefore, we can select the regions of the parameter in which the methods behave more efficiently when they are applied for solving nonlinear equations or the regions in which the schemes have chaotic behavior.
