  The fully discrete problem for convection-diffusion equation is considered.
It comprises compact approximations for spatial discretization, and
Crank-Nicolson scheme for temporal discretization. The expressions for the
entries of inverse of tridiagonal Toeplitz matrix, and Gerschgorin circle
theorem have been applied to locate the eigenvalues of the amplification
matrix. An upper bound on the condition number of a relevant matrix is derived.
It is shown to be of order $\mathcal{O}\left(\frac{\delta v}{\delta
z^2}\right)$, where $\delta v$ and $\delta z$ are time and space step sizes
respectively. Some numerical illustrations have been added to complement the
theoretical findings.
