Robin coefficient identification for a time-fractional diffusion equation |
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Authors: | T. Wei Z.Q. Zhang |
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Affiliation: | School of Mathematics and statistics, Lanzhou University, Gansu, P.R. China. |
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Abstract: | This paper is devoted to a Robin coefficient identification problem for one-dimensional time-fractional diffusion equation. Based on the separation of variables, we transform the identification problem into a nonlinear Volterra integral equation of the first kind with the Robin coefficient and the Dirichlet data on a part of boundary as unknown functions. Then, we use a boundary element method to discrete the first kind integral equation and obtain a nonlinear system of algebraic equations. The conjugate gradient method is applied to solve a regularized optimization problem and finally, we obtain a suitable regularized approximation to the Robin coefficient. Three numerical examples are provided to show the effectiveness and robustness of the proposed method. |
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Keywords: | Robin coefficient identification fractional diffusion equation boundary element method conjugate gradient method |
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