A fractional Landweber iteration method for simultaneous inversion in a time-fractional diffusion equation. (English) Zbl 07921266
Summary: In the present paper, we study the problem to identify the space-dependent source term and initial value simultaneously for a time-fractional diffusion equation. This inverse problem is ill-posed, and we use the idea of decoupling to turn it into two operator equations based on the Fourier method. To solve the inverse problem, a fractional Landweber regularization method is proposed. Furthermore, we present convergence estimates between the exact solution and the regularized solution by using the a-priori and the a-posteriori parameter choice rules. In order to verify the accuracy and efficiency of the proposed method, several numerical examples are constructed.
MSC:
| 41A28 | Simultaneous approximation |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
time-fractional diffusion equation; simultaneous inversion; fractional Landweber iteration; a-priori and a-posteriori regularization parametersReferences:
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