On a numerical solution of the Cauchy problem for the Laplace equation by the fundamental solutions method |
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| Authors: | Takashi Ohe Katsu Yamatani Kohzaburo Ohnaka |
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| Affiliation: | 1. Department of Urban Science, Meijo University, Kani 509-0261, Japan;2. Department of Applied Physics, Graduate School of Engineering, Osaka University, Suita, 565-0871, Japan |
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| Abstract: | We discuss a numerical method to solve a Cauchy problem for the Laplace equation in the two-dimensional annular domain. We consider the case that the Cauchy data is given on an arc. We develop an approximation method based of the fundamental solutions method using the least squares method with Tikhonov regularization. The effectiveness of our method is examined by a numerical experiment. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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