Convergence of the alternating direction method for the numerical solution of a heat conduction equation with delay

Two-dimensional parabolic equations with delay effects in the time component are considered. An alternating direction scheme is constructed for the numerical solution of these equations. The question on the reduction of a problem with inhomogeneous boundary conditions to a problem with homogeneous boundary conditions is considered. The order of approximation error for the alternating direction scheme, stability, and convergence order are investigated.