Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation

We propose an iterative solution method for an implicit finite-difference analog of the inverse problem of identifying the diffusion coefficient in an initial boundary value problem for the subdiffusion equation with the fractional Caputo time derivative. We consider the two different ways of setting the overdetermination condition at the final time point: the value of the solution at some given point and a weighted integral of the solution. The results of numerical implementation of the iterative method are presented on model problems with exact solutions. These results confirm the sufficiently high accuracy of the method.