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

被引：6

作者：

Mrityunjoy, B. ^{[1
]}

Natesan, S. ^{[1
]}

Sendur, A. ^{[2
]}

机构：

[1] Indian Inst Technol, Dept Math, Gauhati 781039, India

[2] Alanya Alaaddin Keykubat Univ, Dept Math Educ, Antalya, Turkey

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2023年 / 100卷 / 02期

关键词：

Singularly perturbed 2D parabolic convection-reaction-diffusion problem; alternating direction implicit scheme; finite difference scheme; Shishkin meshes; stability; uniform error estimate; FINITE-DIFFERENCE SCHEME; MESH;

D O I：

10.1080/00207160.2022.2114077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：253 / 282

页数：30

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