King-Type Derivative-Free Iterative Families: Real and Memory Dynamics. (31st October 2017)

• Record Type: Journal Article
• Authors: Chicharro, F. I.; Cordero, A.; Torregrosa, J. R.; Vassileva, M. P.
• Other Names: Caldarelli Guido Academic Editor.
• Is Part Of: Complexity. Volume 2017(2017)
• Publication Date: 2017-10-31
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2017/2713145
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.