On convergence of the difference schemes for parabolic equation with a source non-local in time

In the work for parabolic equation with non-local in the time source the difference scheme of approximation order is built $O (h^2 + \tau)$, where $h, \tau$ - are the array pitch in space and time coordinate. For solving the examined task prior estimates in differential and difference treatments are obtained. Hence we’ve got the convergence of the difference scheme. Case of equation with a source non-local in time is analyzed.