数学理论与应用2024,Vol.44Issue(3) :50-66.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

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

吕博睿 楚雪 王海军
数学理论与应用2024,Vol.44Issue(3) :50-66.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

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

吕博睿 1楚雪 2王海军2
扫码查看

作者信息

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

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.

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.

关键词

非线性方程组/六阶方法/局部收敛性/吸引域

Key words

Nonlinear equation/Sixth order method/Local convergence/Basin of attraction

引用本文复制引用

基金项目

National Natural Science Foundation of China(12271518)

Key Program of the National Natural Science Foundation of China(62333016)

出版年

2024
数学理论与应用
湖南省数学学会

数学理论与应用

影响因子:0.281
ISSN:1006-8074
段落导航相关论文