Stable numerical solution of an inverse coefficient problem for a time fractional reaction-diffusion equation‎

‎In this paper‎, ‎an inverse problem of determining an unknown reaction coefficient in a one-dimensional time-fractional reaction-diffusion equation is considered‎. ‎This inverse problem is generally ill-posed‎. ‎For this reason‎, ‎the mollification regularization technique with the generalized cross-validation criteria will be employed to find an equivalent stable problem‎. ‎Afterward‎, ‎a finite difference marching scheme is introduced to solve this regularized problem‎. ‎The stability and convergence of the numerical solution are investigated‎. ‎In the end‎, ‎some numerical examples are presented to verify the ability and effectiveness of the proposed algorithm‎.

کلیدواژه ها:

‎Inverse problem‎ ، ‎Time fractional reaction-diffusion equation‎ ، ‎Caputo's fractional derivative‎ ، ‎Mollification‎ ، ‎Marching scheme‎