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

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.