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一种新的正则化方法求解热传导方程的侧边值问题

柏恩鹏 熊向团

柏恩鹏, 熊向团. 一种新的正则化方法求解热传导方程的侧边值问题[J]. 应用数学和力学, 2021, 42(5): 541-550. doi: 10.21656/1000-0887.410290
引用本文: 柏恩鹏, 熊向团. 一种新的正则化方法求解热传导方程的侧边值问题[J]. 应用数学和力学, 2021, 42(5): 541-550. doi: 10.21656/1000-0887.410290
BAI Enpeng, XIONG Xiangtuan. A New Regularization Method for Solving Sideways Heat Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 541-550. doi: 10.21656/1000-0887.410290
Citation: BAI Enpeng, XIONG Xiangtuan. A New Regularization Method for Solving Sideways Heat Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 541-550. doi: 10.21656/1000-0887.410290

一种新的正则化方法求解热传导方程的侧边值问题

doi: 10.21656/1000-0887.410290
基金项目: 国家自然科学基金(11661072)
详细信息
    作者简介:

    柏恩鹏(1995—),男,硕士生(E-mail: baiepnwnu@163.com);熊向团(1977—),男,教授,博士生导师(通讯作者. E-mail: xiongxt@fudan.edu.com).

  • 中图分类号: O241.1

A New Regularization Method for Solving Sideways Heat Equations

Funds: The National Natural Science Foundation of China(11661072)
  • 摘要: 考虑了四分之一平面内的热传导方程的侧边值问题,这类问题是严重不适定的.采用传统拟逆方法得到该问题的一个近似解,但发现它并不是一个正则化解.有趣的是,对解的分母项加以修正便可以得到侧边值问题的一个正则化解,进而提出了一种新的正则化方法,并分别给出先验和后验两种正则化参数选取规则下的Hlder型误差估计.数值实验验证了所提方法的可行性和有效性.
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出版历程
  • 收稿日期:  2020-09-24
  • 修回日期:  2020-12-12
  • 刊出日期:  2021-05-01

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