The modified regularization method for identifying the unknown source on Poisson equation |
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Authors: | Fan Yang Chu-Li Fu |
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Institution: | a School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, People’s Republic of China b School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China |
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Abstract: | This paper discusses the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation from one supplementary temperature measurement at an internal point. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the modified regularization method. For the regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is given. Numerical results are presented to illustrate the accuracy and efficiency of this method. |
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Keywords: | Ill-posed problem Unknown source Modified regularization Poisson equation |
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