Alternating direction implicit method for singularly perturbed 2D parabolic convection–diffusion–reaction problem with two small parameters. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: B., Mrityunjoy; Natesan, S.; Sendur, A.
• Is Part Of: International journal of computer mathematics. Volume 100:Issue 2(2023)
• Page Start: 253
• Page End: 282
• Publication Date: 2023-02-01
• Subjects: Singularly perturbed 2D parabolic convection–reaction–diffusion problem -- alternating direction implicit scheme -- finite difference scheme -- Shishkin meshes -- stability -- uniform error estimate; 65M06 -- 65M12 -- 65M15; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2022.2114077
• Languages: English
• ISSNs: 0020-7160

Abstract

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.