An efficient finite difference method for coupled systems of singularly perturbed parabolic convection-diffusion problems

Abstract

We construct an efficient finite difference method for coupled systems of singularly perturbed parabolic problems of convection-diffusion type. We consider two splitting schemes on a uniform mesh to discretize in time and an upwind scheme on layer-adapted Shishkin and Bakhvalov meshes to discretize in space. The numerical method is proved to be convergent independent of the perturbation parameters. The splitting schemes are very efficient, as at each time level the components of the vector approximate solution are decoupled, which resulted in a reduced computational cost. Numerical results for two test examples are presented that validate the theoretically proved results and also illustrate the efficiency of the proposed finite difference method.

Keywords:

• Singularly perturbed
• convection-diffusion problems
• splitting schemes
• upwind scheme
• layer-adaptive meshes
• uniform convergence

2020 Mathematics Subject Classifications:

• 65M06
• 65M12
• 65M15

Disclosure statement

No potential conflict of interest was reported by the author(s).