  Fourth-order accurate compact schemes for variable coefficient convection
diffusion equations are considered. A sufficient condition for the stability of
the fully discrete problem is derived using a difference equation based
approach. The constant coefficient problems are considered as a special case,
and the unconditional stability of compact schemes for such case is proved
theoretically. The condition number of the amplification matrix is also
analyzed, and an estimate for the same is derived. The examples are provided to
support the assumption taken to assure stability.
