Reaction Coefficient Identification Problem for a Time-Fractional Diffusion Equation

In this paper, we examine the recovery of a space-dependent reaction coefficient for a one-dimensional linear reaction-diffusion equation. The diffusion problem is coupled with a reading of the solution profile at a specified time. Our recovery approach is based on the pseudo-spectral method which is used to formulate a system of time-fractional differential equations involving Fourier coefficients of the solution as well as those of the reaction-coefficient. The resulting differential system is discretized by an exponential time differencing type scheme to obtain a linear algebraic system whose solution approximates the Fourier coefficients of the reaction coefficient. Numerical experiments are presented to illustrate the performance of the proposed method.