Convergence and dynamical study of a new sixth order convergence iterative scheme for solving nonlinear systems-Reference-Cited by-同舟云学术

Convergence and dynamical study of a new sixth order convergence iterative scheme for solving nonlinear systems

Published:2023 Issue:6 Volume:8 Page:12751-12777
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Capdevila Raudys R.¹²,Cordero Alicia¹,Torregrosa Juan R.¹

Affiliation:

1. Institute of Multidisciplinary Mathematics, Universitat Politècnica de València, Valencia, Spain

2. Colegio Politécnico de Ciencias e Ingeniería, Universidad San Francisco de Quito, Ecuador

Abstract

<abstract><p>A novel family of iterative schemes to estimate the solutions of nonlinear systems is presented. It is based on the Ermakov-Kalitkin procedure, which widens the set of converging initial estimations. This class is designed by means of a weight function technique, obtaining 6th-order convergence. The qualitative properties of the proposed class are analyzed by means of vectorial real dynamics. Using these tools, the most stable members of the family are selected, and also the chaotical elements are avoided. Some test vectorial functions are used in order to illustrate the performance and efficiency of the designed schemes.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference34 articles.

1. R. H. Al-Obaidi, M. T. Darvishi, A comparative study on qualification criteria of nonlinear solvers with introducing some new ones, J. Math., 2022 (2022), 1–20. https://doi.org/10.1155/2022/4327913

2. S. Artidiello, A. Cordero, J. R. Torregrosa, M. P. Vassileva, Multidimensional generalization of iterative methods for solving nonlinear problems by means of weight-function procedure, Appl. Math. Comput., 268 (2015), 1064–1071. https://doi.org/10.1016/j.amc.2015.07.024

3. R. Behl, I. K. Argyros, F. O. Mallawi, Some high-order convergent iterative procedures for nonlinear systems with local convergence, Mathematics, 9 (2021), 1–13. https://doi.org/10.3390/math9121375

4. R. Behl, S. Bhalla, A. A. Magreñán, S. Kumar, An efficient high order iterative scheme for large nonlinear systems with dynamics, J. Comput. Appl. Math., 404 (2022), 113249. https://doi.org/10.1016/j.cam.2020.113249

5. D. A. Budzko, A. Cordero, J. R. Torregrosa, New family of iterative methods based on the Ermakov-Kalitkin scheme for solving nonlinear systems of equations, Comput. Math. Math. Phys., 55 (2015), 1947–1959. https://doi.org/10.1134/S0965542515120040

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Optimal Combination of the Splitting–Linearizing Method to SSOR and SAOR for Solving the System of Nonlinear Equations;Mathematics;2024-06-11