  A singularly perturbed parabolic problem of convection-diffusion type with a
discontinuous initial condition is examined. An analytic function is identified
which matches the discontinuity in the initial condition and also satisfies the
homogenous parabolic differential equation associated with the problem. The
difference between this analytical function and the solution of the parabolic
problem is approximated numerically, using an upwind finite difference operator
combined with an appropriate layer-adapted mesh. The numerical method is shown
to be parameter-uniform. Numerical results are presented to illustrate the
theoretical error bounds established in the paper.
