Wide stability in a new family of optimal fourth-order iterative methods

"This is the peer reviewed version of the following article: Chicharro, F. I., Cordero, A., Garrido, N., & Torregrosa, J. R. (2019). Wide stability in a new family of optimal fourth-order iterative methods. Computational and Mathematical Methods, 1(2), e1023, which has been published in final form at https://doi.org/10.1002/cmm4.1023. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] A new family of two¿steps fourth¿order iterative methods for solving nonlinear equations is introduced based on the weight functions procedure. This family is optimal in the sense of Kung¿Traub conjecture and it is extended to design a class of iterative schemes with four step and seventh order of convergence. We are interested in analyzing the dynamical behavior of different elements of the fourth¿order class. This analysis gives us important information about the stability of these members of the family. The methods are also tested with nonlinear functions and compared with other known schemes. The results show the good features of the introduced class.This research was partially supported by the Ministerio de Ciencia, Innovación y Universidades PGC-2018-095896-B-C22 and by the Generalitat Valenciana PROMETEO/2016/089. The authors also want to thank the anonymous referees for their suggestions and comments that have improved the final version of this paper.Chicharro López, FI.; Cordero Barbero, A.; Garrido-Saez, N.; Torregrosa Sánchez, JR. (2019). Wide stability in a new family of optimal fourth-order iterative methods. Computational and Mathematical Methods. 1(2):1-14. https://doi.org/10.1002/cmm4.1023S1141