A finite-difference scheme for a coupled system of singularly perturbed time-dependent reaction–diffusion equations with discontinuous source terms

Abstract

In this paper, a coupled system of singularly perturbed parabolic one-dimensional reaction–diffusion equations with discontinuous source terms is considered. To obtain a reliable approximation of the system solution, we construct a numerical method by using an effective finite-difference scheme which involves a suitable layer-adapted piecewise-uniform Shishkin mesh. We show that the approximations provided by the proposed numerical method converge uniformly with respect to the singular perturbation parameter. The performance of the singularly perturbed parabolic system successfully tested illustrates the agreement with the theoretical results.

Keywords:

• Singularly perturbed problem
• finite-difference scheme
• reaction–diffusion system
• discontinuous source terms
• Shishkin mesh

2010 AMS Subject Classifications:

• 65N06
• 65N22
• 35B25

Disclosure statement

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

Additional information

Funding

The first and second authors wish to acknowledge the SERB-DST, New Delhi (India), for its financial support.