基于中心差商的一类避免求导的非线性方程迭代算法
A Class of Iterative Algorithms for Nonlinear Equations Without Derivation Based on Central Difference
郭巧 1杨兵 1王伟昌2
作者信息
- 1. 安徽职业技术学院,安徽合肥 230611
- 2. 安徽工布智造工业科技有限公司,安徽合肥 238000
- 折叠
摘要
非线性方程求解的迭代方法中比较经典的牛顿迭代法、改进牛顿法等,虽然能够提高迭代效率,但因为需要对非线性方程求导并要求导数不能为零,使得其在实际应用中具有一定的局限性.文章基于开依沙尔·热合曼等人提出的四阶收敛迭代格式,利用中心差商近似代替一阶导数,通过对加权因子进行赋值,得到一类避免求导的四阶收敛的迭代算法.收敛性分析和数值实例证明该方法适用于大多数非线性方程的求根问题,在工程计算方面具有一定的实用价值.
Abstract
The classical iterative methods for solving nonlinear equations,such as Newton's iterative method and improved Newton's method,can improve the efficiency of iteration but have limitations in practical applications because they require derivatives of nonlinear equations and the derivatives cannot be zero.Based on the fourth-order convergent iterative format proposed by Kaishal-Rehman et al,the article obtains a class of fourth-order convergent iterative algorithms that can avoid derivatives by using the central difference quotient approximation instead of the first-order derivatives and assigning weight-ing factors.convergence analysis and numerical examples demonstrates that the methods should be applied to most nonlinear equation in finding root problems,and that they have a certain practical value in engineering calculation.
关键词
中心差商/非线性方程/避免求导/四阶收敛Key words
central difference quotient/nonlinear equations/avoiding derivative/fourth-order convergence引用本文复制引用
基金项目
安徽省高等学校科研项目(2023)(2023AH040192)
安徽省高等学校科研项目(2023)(2023AH051443)
职业院校数字化转型行动研究项目(2022)(KT22086)
安徽省职业技术学院质量工程项目(2022)(2022yjjxyj05)
出版年
2024
NETL
NSTL
万方数据