A simplified Tikhonov regularization method for determining the heat source |
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Authors: | Fan Yang Chu-Li Fu |
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Affiliation: | 1. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, People’s Republic of China;2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China |
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Abstract: | This paper is to discuss the inverse problem of determining a spacewise dependent heat source in one-dimensional heat equation in a bounded domain where data is given at some fixed time. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. The regularization solution is given by a simplified Tikhonov regularization. For this regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is obtained. Numerical examples show that the regularization method is effective and stable. |
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Keywords: | Heat source Simplified Tikhonov Error estimate |
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