Computational Method for Singularly Perturbed Parabolic Problem

Singularly perturbed parabolic problem with initial and boundary value is considered. The computational method, which is combining techniques of asymptotic method and numerical method, is constructed. Firstly, the analytic solution is decomposed into the smooth component and the singular component. Secondly, the non-equidistant mesh partition in space direction according to Shishkin's transition point is considered. Half of the mesh number are placed in the boundary layer, another half of mesh number are placed outside the boundary layer. Equidistant mesh partition in time direction is considered. Thirdly, upwind difference method is applied for the smooth component, which is the normal differential equation. For the singular component, the exponentially fitted difference scheme with zero approximate technique is used. Computational errors are estimated. The new method solve the problem very well. Finally, numerical experiment is given, which is in agreement with the theoretical result.