Spectral regularization method for solving a time-fractional inverse diffusion problem |
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Authors: | G.H. ZhengT. Wei |
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Affiliation: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China |
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Abstract: | In this paper, we consider an inverse problem for a time-fractional diffusion equation with one-dimensional semi-infinite domain. The temperature and heat flux are sought from a measured temperature history at a fixed location inside the body. We show that such problem is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective. |
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Keywords: | Spectral regularization Time-fractional inverse diffusion Caputo&rsquo s fractional derivatives Temperature Heat flux Fourier transform Laplace transform |
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