Determination of an Unknown Diffusion Coefficient in a Parabolic Inverse Problem

In this thesis we studied the finite difference approximation for the solution of one dimensional parabolic inverse problem of finding the function ( ) and the unknown positive coeffient ( ) . The Backward time centered space (BTCS) which is unconditionally stable is studied and it’s 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 the concluding remark are presented. Keywords: finite difference methods, parabolic inverse problem, convergence, Error estimates, maximum principle.