Parameter-uniform finite difference scheme for a system of coupled singularly perturbed convection–diffusion equations

Abstract

In this paper, we discuss the parameter-uniform finite difference method for a coupled system of singularly perturbed convection–diffusion equations. The leading term of each equation is multiplied by a small but different magnitude positive parameter, which leads to the overlap and interact boundary layer. We analyze the boundary layer and construct a piecewise-uniform mesh on the variant of the Shishkin mesh. We prove that our schemes converge almost first-order uniformly with respect to small parameters. We present some numerical experiments to support our theoretical analysis.

Keywords:

• Convection–diffusion
• Singular perturbation
• Solution decomposition
• Shishkin mesh
• Upwind difference scheme

Acknowledgement

The work was supported by National Natural Science Foundation (Grant Nos 10301029 and 10241003) of China.