ON THE CHOICE OF INITIAL CONDITIONS OF DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS

when the exact solution belongs to the anisotropic Sobolev spaceWe consider the first initial-boundary value problem for linear heat conductivity equation with constant coefficient in Omega x (0, T], where Omega is a unit square. A high order accuracy ADI two level difference scheme is constructed on a 18-point stencil using Steklov averaging operators. We prove that the finite difference scheme converges in the discrete L2 -norm with the convergence rate O(h(s) + T-s/2), when the exact solution belongs to the anisotropic Sobolev space W-2(s,s/2) , s epsilon (2, 4].