Boundary layer resolving pseudospectral methods for singular perturbation problems

Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary differential equations (ODEs) which possess boundary layers. It is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions. We introduce here a new effective procedure based on coordinate stretching and the Chebyshev pseudospectral method to resolve the boundary layers. Stable and accurate results are obtained for very thin boundary layers with a fairly small number of spectral collocation points.