On the second order implicit difference schemes for a right hand side identification problem

In many physical phenomena, especially in temperature over-specification partial differential equation with an unknown source function appears. The present paper is devoted to the study of the well-posedness of the approximate solution of a right-hand side identification problem for a parabolic equation. The second order of accuracy implicit difference scheme is presented. The coercive stability estimates for the solution of this difference scheme are obtained. The theoretical statements for the solution of this difference schemes are supported by results of numerical experiments.