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

作　　者：郭巧 杨兵[1] 王伟昌 Guo Qiao;Yang Bing;Wang Weichang(Anhui Vocational and Technical College,Hefei 230611,China;Anhui Gongbu Zhizao Industrial Technology Co.,Ltd.,Hefei 238000,China)

机构地区：[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

出　　处：《廊坊师范学院学报（自然科学版）》2024年第1期18-22,共5页Journal of Langfang Normal University(Natural Science Edition)

基　　金：2023年安徽省高校科研项目(2023AH040192,2023AH051443);2022年职业院校数字化转型行动研究项目(KT22086);2022年安徽省职业技术学院质量工程项目(2022yjjxyj05)。

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。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 weighting 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 

分 类 号：O241.3[理学—计算数学]