Before revision:  We also  give an example of extending a compact scheme for non-uniform in space and time rectangular meshes.
After revision:  We also transform an unconditionally stable 4th order two-level scheme suggested for n=2 to the three-level form, extend it for any n\geq 1 and prove its stability. We also give an example of extending a compact scheme for non-uniform in space and time rectangular meshes.