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Robin coefficient identification for a time-fractional diffusion equation. (English) Zbl 1342.65210

Summary: 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.

MSC:

65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
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