Simultaneous Inversion for Space-Dependent Diffusion Coefficient and Source Magnitude in the Time Fractional Diffusion Equation

Dali Zhang, Gongsheng Li, Xianzheng Jia, Huiling Li


We deal with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the source magnitude in the time fractional diffusion equation from viewpoint of numerics. Such simultaneous inversion problem is often of severe ill-posedness as compared with that of determining a single coefficient function. The forward problem is solved by employing an implicit finite difference scheme, and the inverse problem is solved by applying the homotopy regularization algorithm with Sigmoid-type homotopy parameter. The inversion solutions approximate to the exact solutions demonstrating that the proposed algorithm is efficient for simultaneous inversion problems in the fractional diffusion equation.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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