Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers

Abstract

In this paper, fitted mesh numerical scheme is presented for solving singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers. To approximate the solution, we discretize the temporal variable on uniform mesh and discretize the spatial one on piecewise uniform mesh of the Shishkin mesh type. The resulting scheme is shown to be almost first order convergent that accelerated to almost second order convergent by applying the Richardson extrapolation technique. Stability and consistency of the proposed method are established very well in order to guarantee the convergence of the method. Further, the theoretical investigations are confirmed by numerical experiments. Moreover, the present scheme is stable, consistent and gives more accurate solution than existing methods in the literature.