二维Helmholtz方程不适定问题的一种算子软化正则法

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二维Helmholtz方程不适定问题的一种算子软化正则法何尚琴^1,2, 冯秀芳²1 北方民族大学数学与信息科学学院银川 750021;
2 宁夏大学数学统计学院银川 750021 An Operator Mollification Method to Ill-posed Problem for Two-dimensional Helmholtz Equation Shang Qin HE^1,2, Xiu Fang FENG²1 School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, P. R. China;
2 School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P. R. China

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摘要本文研究带有混合边界的二维Helmholtz方程不适定问题.为了获得稳定的数值解，利用基于de la ValléePoussin算子的软化正则方法，得到了正则近似解，给出正则近似解与精确解之间在先验参数选取规则之下的误差估计，并通过数值实验检验了数据有噪声扰动时方法的有效性和稳定性.

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收稿日期: 2019-01-21

MR (2010):

O241.8

基金资助:国家自然科学基金资助项目（11961054）

通讯作者:冯秀芳E-mail: xf_feng@nxu.edu.cn

作者简介: 何尚琴,E-mail:hsq@nxu.edu.cn

引用本文:

何尚琴, 冯秀芳. 二维Helmholtz方程不适定问题的一种算子软化正则法[J]. 数学学报, 2020, 63(6): 545-556. Shang Qin HE, Xiu Fang FENG. An Operator Mollification Method to Ill-posed Problem for Two-dimensional Helmholtz Equation. Acta Mathematica Sinica, Chinese Series, 2020, 63(6): 545-556.

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