Alternating direction implicit method for singularly perturbed 2D parabolic convection-diffusion-reaction problem with two small parameters

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 O(N-1 In N + M-1), where N, M are the spatial and temporal parameters respectively. Numerical experiments confirm the theoretical results and the effectiveness of the proposed method.