We consider the Rothe difference scheme for approximate solution of the abstract parabolic equation in a Hilbert space with the nonlocal boundary condition. Theorems on stability estimates, coercivity and almost coercivity estimates for the solution of this difference scheme are established. In application, new coercivity inequalities for the solution of multi-point nonlocal boundary value difference equations of parabolic type are obtained. تفاصيل المقالة