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We consider several finite difference approximation to an inverse problem of determining an unknown source parameter $p(t)$ which is a coefficient of the solution $u$ in a linear parabolic equation subject to additional information on the solution integral type along with the usual initial boundary conditions. The backward Euler scheme is studied and its covergence is proved via an application of the discrete maximum principle for a transformed problem. Error estimates for $u$ and $p$ involve numerical differentiation of the approximation to the transformed problem. Some experimental numerical results using the newly proposed numerical procedure are discussed.
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