Affiliation:
1. Instituto de Matemática Multidisciplinar Universitat Politècnica de València Valencia Spain
Abstract
In this work, we modify the iterative structure of Traub's method to include a real parameter
. A parametric family of iterative methods is obtained as a generalization of Traub, which is also a member of it. The cubic order of convergence is proved for any value of
. Then, a dynamical analysis is performed after applying the family for solving a system cubic polynomials by means of multidimensional real dynamics. This analysis allows to select the best members of the family in terms of stability as a preliminary study to be generalized to any nonlinear function. Finally, some iterative schemes of the family are used to check numerically the previous developments when they are used to approximate the solutions of academic nonlinear problems and a chemical diffusion reaction problem.
Subject
General Engineering,General Mathematics
Reference17 articles.
1. Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension?;Cordero A.;Appl. Math. Comput.,2014
2. Seventh-order derivative-free iterative method for solving nonlinear systems
3. Increasing the order of convergence for iterative methods to solve nonlinear systems
4. Developing high order methods for the solution of systems of nonlinear equations;Chun C.;Appl. Math. Comput.,2019
5. Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications