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The method of central difference for the inverse time-dependent heat source problem |
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| Authors: | Fan Yang HengZhen GuoXiaoXiao Li |
| Institution: | a School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China b School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, People’s Republic of China c Institute of Education, Lanzhou City University, Lanzhou, Gansu 730070, People’s Republic of China |
| Abstract: | This paper investigates the inverse problem of determining a heat source in a parabolic equation where data are given at some fixed location. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. A central difference regularization method is given and an order optimal stability estimate is obtained. Numerical results for several benchmark test problems indicate that the central difference regularization method is an accurate and flexible method to determine the unknown time-dependent heat source. |
| Keywords: | Method of central difference Time-dependent heat source Error estimate |
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