Abstract: In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter ε is given, and error estimate and numerical result are also given.

Key words: nonsmooth boundary layer, characteristic boundary, nonuniform mesh, exponentially fitted, uniformly convergent difference scheme, parabolic differential equation