摘要
该文通过引入基于模的非线性函数,推广了经典牛顿算法,构造了一个具有高阶收敛性的加速牛顿法来求解一类源于自由边值问题离散的弱非线性互补问题.理论上详细地分析了其收敛效率.数值实验充分验证了所提出算法的可行性和有效性.
In this paper,by introducing the modulus-based nonlinear function and extending the classical Newton method,we investigate an accelerated Newton iteration method with highorder convergence for solving a class of weakly nonlinear complementarity problems which arise from the discretization of free boundary problems.Theoretically,the performance of high-order convergence is analyzed in details.Some numerical experiments illustrate the feasibility and efficiency of the proposed method.
作者
谢亚君
马昌凤
Yajun Xie;Changfeng Ma(School of Big Data,Fuzhou University of International Studies and Trade&Engineering Research Center of Universities of Fujian Province,Fuzhou 350202)
出处
《数学物理学报(A辑)》
CSCD
北大核心
2022年第5期1506-1516,共11页
Acta Mathematica Scientia
基金
福建省自然科学基金(2019J01879)
中国科学院大学重点研发项目(H2020003(20A01246ZY))
省重大教改项目(FBJG20200310)
新工科研究实践项目(J15934 19745784GS)。
关键词
弱非线性互补问题
高阶收敛性
基于模的非线性函数
自由边值问题
加速牛顿法
Weakly nonlinear complementarity problems
High-order convergence
The modulus-based nonlinear function
Free boundary problems
Accelerated Newton method