Alternating direction implicit method for singularly perturbed 2D parabolic convection–diffusion–reaction problem with two small parameters. Issue 2 (1st February 2023) - B., Mrityunjoy; Natesan, S.; Sendur, A.
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 O ( N − 1 ln ⁡ 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.