A hybrid approximation scheme for 1-D singularly perturbed parabolic convection-diffusion problems

Abstract

Our study is concerned with a hybrid spectral collocation approach to solve the singularly perturbed $1$-D parabolic convection-diffusion problems. In this approach, discretization in time is carried out with the help of Taylor series expansions before the spectral based on novel special polynomials is applied for the spatial operator in the time step. A detailed error analysis of the presented technique is carried out with regard to the space variable. The advantages of this attempt are presented through comparison of our results in the model problems obtained by this technique and other existing schemes.