ABSTRACT
In this article, we construct and analyse an Alternating Direction Implicit (ADI) scheme for singularly perturbed 2D parabolic convection–diffusion–reaction problems with two small parameters. We consider the operator-splitting ADI finite difference scheme for time stepping on a uniform mesh and a simple upwind-difference scheme for spatial discretization on a specially designed piecewise-uniform Shishkin mesh. The resulting scheme is proved to be uniformly convergent of order , where N, M are the spatial and temporal parameters respectively. Numerical experiments confirm the theoretical results and the effectiveness of the proposed method.
Acknowledgements
The authors wish to acknowledge the anonymous referees for carefully reading the manuscript and providing their valuable comments and suggestions, which really helped to improve the presentation.
Disclosure statement
No potential conflict of interest was reported by the authors.