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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (3): 77-84.doi: 10.6040/j.issn.1671-9352.0.2022.304

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后验参数软化法求解Helmholtz方程柯西问题

李振平1,2,余亚辉1*   

  1. 1.洛阳理工学院数学与物理教学部, 河南 洛阳 471023;2.西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2023-03-02
  • 作者简介:李振平(1982— ),女,博士研究生,研究方向为应用偏微分方程及数值解. E-mail:henanlizhp@163.com*通信作者简介:余亚辉(1982— ),男,硕士,副教授,研究方向为应用数学. E-mail:yuyahui@lit.edu.cn
  • 基金资助:
    河南省高等学校青年骨干教师培养计划资助项目(2019GGJS241)

A mollification method with a posteriori parameter selection for solving the Cauchy problem of the Helmholtz equation

LI Zhen-ping1,2, YU Ya-hui1*   

  1. 1. Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, Henan, China;
    2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2023-03-02

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摘要： 为了恢复解的稳定性,提出一种基于Gauss核的后验参数软化正则化方法,得到精确解与近似解之间的稳定性误差估计,并作数值实验,验证了该方法的有效性。

关键词: Helmholtz方程的柯西问题, 软化方法, 后验参数选取, 误差估计

Abstract: In order to restore the stability of the solution, a mollification regularization method with a posteriori selection of regularization parameter based on Gaussian kernel function is proposed. The stability error estimate between the exact solution and its approximation solution is obtained. Numerical experiments are carried out to verify the effectiveness of the proposed method.

Key words: Cauchy problem for the Helmholtz equation, mollification method, posteriori parameter selection, error estimate

中图分类号: 

  • O241.82
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