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Helmholtz方程Cauchy问题的间接积分方程方法

本站小编 Free考研考试/2021-12-27

孙瑶, 陈博
中国民航大学理学院数学系, 天津 300300
收稿日期:2017-04-02出版日期:2018-09-15发布日期:2018-08-08


基金资助:国家自然科学基金(项目号:11501566)和中央高校基本科研业务费(项目号:3122017078).


INDIRECT BOUNDARY INTEGRAL EQUATION METHOD FOR THE CAUCHY PROBLEM OF THE HELMHOLTZ EQUATION

Sun Yao, Chen Bo
College of science, Civil Aviation University of China, Tianjin 300300, China
Received:2017-04-02Online:2018-09-15Published:2018-08-08







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本文处理二维和三维Helmholtz方程的边界数据复原问题.通过利用位势理论近似问题的解,导出了解决Cauchy问题的一种非迭代积分方程方法.为了处理形成问题的不适定性,采用了Tikhonov正则化结合Morozov偏差原理的方法,并且给出了算法的收敛性和误差估计,最后给出了二维和三维的数值算例.通过数值算例我们检验了源点和边界之间距离的关系,算法关于噪声、源点数目的数值收敛性,稳定性.
MR(2010)主题分类:
65M32

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