On the Local Convergence and Dynamics of New Iterative Method with Sixth Order Convergence

doi:10.3969/j.issn.1006-8074.2024.03.004

Mathematical Theory and Applications ›› 2024, Vol. 44 ›› Issue (3): 50-.doi: 10.3969/j.issn.1006-8074.2024.03.004

Previous Articles Next Articles

On the Local Convergence and Dynamics of New Iterative Method with Sixth Order Convergence

Lyu Borui^1,2, Chu Xue¹, Wang Haijun^1,*

1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China; 2. China Coal Research Institute Changzhou Automatization Research Institute, Changzhou 213000, China

Online:2024-09-28 Published:2024-11-06
Contact: Wang Haijun, Professor, PhD; E-mail: wanghj@cumt.edu.cn
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 12271518) and the Key Program of the National Natural Science Foundation of China (No. 62333016)

Abstract

Abstract:

In this paper, we construct a new sixth order iterative method for solving nonlinear equations. The local convergence and order of convergence of the new iterative method is demonstrated. In order to check the validity of the new iterative method, we

employ several chemical engineering applications and academic test problems. Numerical results show the good numerical performance of the new iterative method. Moreover, the dynamical study of the new method also supports the theoretical results.

Key words: Nonlinear equation, Sixth order method, Local convergence, Basin of attraction

Lyu Borui, Chu Xue, Wang Haijun. On the Local Convergence and Dynamics of New Iterative Method with Sixth Order Convergence[J]. Mathematical Theory and Applications, 2024, 44(3): 50-.

[1]	Huan Xiang. The Study of Numerical Solutions to a Class of Overdetermined System of Nonlinear Equations [J]. Mathematical Theory and Applications, 2017, 37(3-4): 17-25.
[2]	Li Weifei. An Inexact Regularized Newton Method for Monotone and Nonlinear Equations and its Local Convergence [J]. Mathematical Theory and Applications, 2016, 36(4): 29-35.
[3]	Wu Peiyu, Zhang Li. An Inexact Broyden Method for Nonlinear Equations [J]. Mathematical Theory and Applications, 2016, 36(2): 1-9.

On the Local Convergence and Dynamics of New Iterative Method with Sixth Order Convergence

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 3

Recommended Articles

Metrics

Comments