新六阶迭代法的局部收敛性和动力学性质分析

doi:10.3969/j.issn.1006-8074.2024.03.004

数学理论与应用 ›› 2024, Vol. 44 ›› Issue (3): 50-.doi: 10.3969/j.issn.1006-8074.2024.03.004

新六阶迭代法的局部收敛性和动力学性质分析

吕博睿^1,2,楚雪¹,王海军^1,*

1. 中国矿业大学数学学院, 徐州, 221116; 2. 中煤科工常州研究院, 常州, 213000

出版日期:2024-09-28 发布日期:2024-11-06

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)

摘要/Abstract

摘要： 本文给出求解非线性方程组的一个六阶迭代算法,在理论上证明算法的局部收敛性和收敛阶. 为了检验新迭代方法的有效性, 我们采用几个化学工程实际问题和学术测试问题进行测试, 数值结果表明新迭代方法具有良好的数值性能. 此外, 新迭代方法的动力学行为也进一步表明了新方法的有效性.

关键词: 非线性方程组, 六阶方法, 局部收敛性, 吸引域

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

吕博睿, 楚雪, 王海军. 新六阶迭代法的局部收敛性和动力学性质分析[J]. 数学理论与应用, 2024, 44(3): 50-.

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]	李维飞. 求解单调非线性方程组的非精确正则化牛顿法及其局部收敛性[J]. 数学理论与应用, 2016, 36(4): 29-35.
[2]	伍佩钰, 张丽. 求解非线性方程组的一种非精确Broyden方法[J]. 数学理论与应用, 2016, 36(2): 1-9.

新六阶迭代法的局部收敛性和动力学性质分析

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

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