源于自由边值离散的弱非线性互补问题的m+1阶收敛性算法

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1506-1516.

源于自由边值离散的弱非线性互补问题的m+1阶收敛性算法

谢亚君(),马昌凤*()

^{福州外语外贸学院大数据学院 & 福建省高校工程研究中心福州 350202}

收稿日期:2021-09-26 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 马昌凤 E-mail:xyj@fzfu.edu.cn;mcf@fzfu.edu.cn
作者简介:谢亚君, E-mail: xyj@fzfu.edu.cn
基金资助:
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)

Algorithm with Order m + 1 Convergence for Weakly Nonlinear Complementarity Problems Derived From the Discretization of Free Boundary Problems

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}

Received:2021-09-26 Online:2022-10-26 Published:2022-09-30
Contact: Changfeng Ma E-mail:xyj@fzfu.edu.cn;mcf@fzfu.edu.cn
Supported by:
the Natural Science Foundation of Fujian Province(2019J01879);the Key Research and Development Projects of University of Chinese Academy of Science(H2020003(20A01246ZY));the Major Educational Reform Projects of Fujian Province(FBJG20200310);the New Engineering Research Practice Project(J15934 19745784GS)

摘要/Abstract

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.

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

Abstract:

In this paper, by introducing the modulus-based nonlinear function and extending the classical Newton method, we investigate an accelerated Newton iteration method with high-order 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.

Key words: Weakly nonlinear complementarity problems, High-order convergence, The modulus-based nonlinear function, Free boundary problems, Accelerated Newton method

中图分类号:

O224.2

谢亚君,马昌凤. 源于自由边值离散的弱非线性互补问题的m+1阶收敛性算法[J]. 数学物理学报, 2022, 42(5): 1506-1516.

Yajun Xie,Changfeng Ma. Algorithm with Order m + 1 Convergence for Weakly Nonlinear Complementarity Problems Derived From the Discretization of Free Boundary Problems[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1506-1516.

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