A parameter-uniform hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems

ABSTRACT

We present the hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems exhibiting overlapping boundary layers. We discretize the time derivative by the backward-Euler method and the spatial derivatives is discretized by the hybrid difference scheme on Shishkin mesh. We have shown that the presented numerical scheme is parameter-uniform convergent of first-order in temporal variable and almost second-order in spatial variable. Numerical experiments supporting the theoretical results are presented.

KEYWORDS:

• Singularly perturbed system
• parabolic convection-diffusion problems
• boundary layers
• piecewise-uniform Shishkin mesh
• hybrid finite difference scheme
• uniform convergence

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 65M12
• CR G1.8

Acknowledgments

The authors express their sincere thanks to the referees whose valuable comments helped to improve the presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Maneesh Kumar Singh  http://orcid.org/0000-0003-2623-5441

Srinivasan Natesan  http://orcid.org/0000-0001-7527-1989