Reconstruction of the Time-Dependent Diffusion Coefficient in a Space-Fractional Parabolic Equation

We propose two algorithms for investigation the numerical reconstruction of the time-dependent diffusion coefficient in a space-fractional parabolic problem at integral and point measured outputs. In the first one, by implicit Euler method we perform a linearization of the quadratically nonlinear initial boundary value problem on each time level. Then, we apply a decomposition to this problem solution around the unknown diffusion coefficient. Finally, using the integral or point observations we express in exact form by the solutions of the new subproblems, the required diffusion coefficient. By the second one, on each time level, an iterative algorithm based on the secant method for the numerical identification of the diffusion coefficient, is proposed. We compare the two methods on computational test examples.