Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition

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