Barman, MrityunjoyNatesan, SrinivasanSendur, Ali2026-01-242026-01-2420250168-92741873-5460https://doi.org/10.1016/j.apnum.2024.08.026https://hdl.handle.net/20.500.12868/5635The solution of the singular perturbation problems (SPP) of convection-diffusion-reaction type may exhibit regular and corner layers in a rectangular domain. In this work, we construct and analyze a parameter-uniform operator-splitting alternating direction implicit (ADI) scheme to efficiently solve a two-dimensional parabolic singularly perturbed problem with two positive parameters. The proposed model is a combination of the backward-Euler method defined on a uniform mesh in time and a hybrid method in space defined on a special Shishkin mesh. The analysis is presented on a layer adapted piecewise-uniform Shishkin mesh. The developed numerical method is proved to be first-order convergent in time and almost second-order convergent in space. The numerical experiments are performed to validate the theoretical convergence results and illustrate the efficiency of the current strategy.eninfo:eu-repo/semantics/closedAccessSingularly perturbed IBVPConvection-diffusion-reactionShishkin meshADI schemeError estimateArticle10.1016/j.apnum.2024.08.0262071111352-s2.0-85203009611Q1WOS:001309040100001Q1