DETERMINATION OF AN UNKNOWN DIFFUSION COEFFICIENT IN A PARABOLIC INVERSE PROBLEM (FUDMA JOURNAL OF SCIENCES, 2022)
In this paper we studied the finite difference scheme for the solution of one dimensional parabolic inverse problem of finding the function  and the unknown positive coefficient . The Backward time centered space (BTCS) which is unconditionally stable is studied and its convergent is proved using application of discrete maximum principle. Error estimates for  and  is studied and to give clear overview of the methodology several model problems are solved numerically. According to the experimental numerical results and the concluding remark are presented
Keywords: finite difference methods, parabolic inverse problem, convergence, Error estimates, maximum principle.