An iteration regularization for a time-fractional inverse diffusion problem. (English) Zbl 1254.65100
Summary: We consider a time-fractional inverse diffusion problem, where data is given at \(x = 1\) and the solution is required in the interval \(0 < x < 1\). This problem is typically ill-posed: the solution (if it exists) does not depend continuously on the data. We give a new iteration regularization method to deal with this problem, and error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Furthermore, numerical implement shows the proposed method works effectively.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
time-fractional inverse diffusion problem; iteration regularization method; A posteriori parameter choice; error estimateReferences:
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