The boundary layer method for the solution of a singular perturbation problem for a parabolic partial differential equation (Q1096775)

We discuss a singular perturbation problem for a parabolic partial differential equation. As usual, we must reduce the mesh size in the neighbourhood of the boundary layer so that the typical feature of the boundary layer will not be lost. Then we need a very large operational quantity when the mesh sizes are getting too small. We propose a boundary layer scheme, which does not take a very fine mesh size in the neighbourhood of the boundary layer. Numerical examples show that sufficient accuracy can be satisfied with moderate step size.