Modified regularization method for the Cauchy problem of the Helmholtz equation |
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Authors: | H.H. Qin T. Wei |
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Affiliation: | School of Mathematics and Statistics, Lanzhou University, Tianshui Road, Lanzhou City, Gansu Provience, PR China |
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Abstract: | In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a modified regularization method to solve it based on the solution given by the method of separation of variables. Convergence estimates are presented under two different a-priori bounded assumptions for the exact solution. Finally, numerical examples are given to show the effectiveness of the proposed numerical method. |
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Keywords: | Cauchy problem Helmholtz equation Regularization method Convergence estimates |
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