A Wavelet-Galerkin method for a singularly perturbed convection-dominated diffusion equation

There are few techniques available to numerically solve singularly perturbed parabolic problems. In this paper we show that the Wavelet-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on several examples and a comparison with the method of reduction order is made. It is shown that the Wavelet-Galerkin method yields better results.