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几类微分-代数方程的神经网络求解法

杨钊 兰钧 吴勇军

杨钊, 兰钧, 吴勇军. 几类微分-代数方程的神经网络求解法[J]. 应用数学和力学, 2019, 40(2): 115-126. doi: 10.21656/1000-0887.390122
引用本文: 杨钊, 兰钧, 吴勇军. 几类微分-代数方程的神经网络求解法[J]. 应用数学和力学, 2019, 40(2): 115-126. doi: 10.21656/1000-0887.390122
YANG Zhao, LAN Jun, WU Yongjun. On Solutions to Several Classes of Differential-Algebraic Equations Based on Artificial Neural Networks[J]. Applied Mathematics and Mechanics, 2019, 40(2): 115-126. doi: 10.21656/1000-0887.390122
Citation: YANG Zhao, LAN Jun, WU Yongjun. On Solutions to Several Classes of Differential-Algebraic Equations Based on Artificial Neural Networks[J]. Applied Mathematics and Mechanics, 2019, 40(2): 115-126. doi: 10.21656/1000-0887.390122

几类微分-代数方程的神经网络求解法

doi: 10.21656/1000-0887.390122
基金项目: 国家自然科学基金(11772293;11272201)
详细信息
    作者简介:

    吴勇军(1978—),男,副研究员(通讯作者. E-mail: yj.wu@sjtu.edu.cn).

  • 中图分类号: O193;O322

On Solutions to Several Classes of Differential-Algebraic Equations Based on Artificial Neural Networks

Funds: The National Natural Science Foundation of China(11772293;11272201)
  • 摘要: 在非线性科学中,寻求微分方程的近似解析解一直是重要的研究课题和研究热点.利用人工神经网络原理,结合最优化方法,研究了几类微分-代数方程的近似解析解,包括指标1,2,3型Hessenberg方程及指标3型Euler-Lagrange方程,得到了方程近似解析解的表达式.通过与精确解或Runge-Kutta(龙格-库塔)数值计算结果对比,表明神经网络方法的结果有很高的精度.
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出版历程
  • 收稿日期:  2018-04-18
  • 修回日期:  2018-11-11
  • 刊出日期:  2019-02-01

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