Efficient High-Order Discretization Methods for Coupled Systems of Singularly Perturbed Parabolic Convection-Diffusion Problems

Abstract

This paper develops efficient high-order convergent discretization methods for coupled systems of singularly perturbed parabolic convection-diffusion problems exhibiting boundary layers. The discretization of the problem consists of two splitting schemes in time on a uniform mesh and a high-order hybrid finite difference scheme in space on appropriate layer-adapted Shishkin mesh. The splitting schemes decoupled the vector approximate solution at each time level, resulting in a reduced computational time. The convergence of the discretization methods is discussed in two steps using the barrier function approach. The proposed methods are proved to be uniformly convergent, having first-order accuracy in time and almost second-order accuracy in space. The splitting schemes are very efficient in comparison with the standard discretization. Numerical results confirm the theoretical findings and illustrate the efficiency of the proposed discretization methods.