科研之友
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摘要
In this paper the Cauchy problem for the Helmholtz equation with inhomogeneous Neumann data is considered. This problem is severely ill-posed, the solution does not depend continuously on the data. An approximate method based on the a posteriori Fourier regularization in the frequency space is analyzed. Some crucial information about the regularization parameter hidden in the a posteriori choice rule are found, and some sharp error estimates between the exact solution and its regularization approximate solution are proved. Numerical examples show the effectiveness of the method. A comparison of numerical effect between the a posteriori and the a priori Fourier method is also taken into account.
