Fourth order accurate compact schemes for variable coefficient
convection-diffusion equations are considered. A sufficient condition for
stability of the schemes have been 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
analysed, and an estimate for the same is derived. In order to verify the
derived conditions numerically, MATLAB codes are provided in Appendix of the
manuscript. An example is provided to support the assumption taken to assure
stability