| 二维Helmholtz方程不适定问题的一种算子软化正则法 |
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| 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,1936,63(6):545-556. |
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| 作者姓名： | 何尚琴 冯秀芳 |
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| 作者单位： | 1.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 |
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| 基金项目： | 国家自然科学基金资助项目（11961054） |
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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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An Operator Mollification Method to Ill-posed Problem for Two-dimensional Helmholtz Equation |
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| Shang Qin HE,Xiu Fang FENG.An Operator Mollification Method to Ill-posed Problem for Two-dimensional Helmholtz Equation[J].Acta Mathematica Sinica,1936,63(6):545-556. |
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| Authors: | Shang Qin HE Xiu Fang FENG |
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| Institution: | 1.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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| Abstract: | In this paper, the ill-posed Cauchy problem for two-dimensional Helmholtz equation with mixed boundary is investigated. To obtain stable numerical solution, a mollification regularization method with the de la Vallée Poussin operator is proposed. Error estimate between the exact solution and its approximation is given under the proper choice of a priori parameter. A numerical experiment shows that our procedure is effective and stable with respect to perturbations of noise in the data. |
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| Keywords: | Helmholtz equation ill-posed de la vallée Poussin operator mollification method error estimate |
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