Mrityunjoy, B.Natesan, S.Sendur, A.2026-01-242026-01-2420230020-71601029-0265https://doi.org/10.1080/00207160.2022.2114077https://hdl.handle.net/20.500.12868/5847In 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.eninfo:eu-repo/semantics/closedAccessSingularly perturbed 2D parabolic convection-reaction-diffusion problemalternating direction implicit schemefinite difference schemeShishkin meshesstabilityuniform error estimateArticle10.1080/00207160.2022.211407710022532822-s2.0-85138314432Q2WOS:000854941800001Q2