Parameter-uniform numerical method for singularly perturbed 2D delay parabolic convection-diffusion problems on Shishkin mesh

被引:8
作者
Das, Abhishek [1 ]
Natesan, Srinivasan [2 ]
机构
[1] ICFAI Univ, Faulty Sci & Technol, Tripura Campus, Agartala 799210, India
[2] Indian Inst Technol, Dept Math, Gauhati 781039, India
关键词
Singularly perturbed 2D delay parabolic problems; Boundary layers; Upwind scheme; Piecewise-uniform Shishkin mesh; Uniform convergence; SCHEME;
D O I
10.1007/s12190-018-1175-y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we study the numerical solution of a singularly perturbed 2D delay parabolic convection-diffusion problem. First, we discretize the domain with a uniform mesh in the temporal direction and a special mesh in the spatial directions. The numerical scheme used to discretize the continuous problem, consists of the implicit-Euler scheme for the time derivative and the classical upwind scheme for the spatial derivatives. Stability analysis is carried out, and parameter-uniform error estimates are derived. The proposed scheme is of almost first-order (up to a logarithmic factor) in space and first-order in time. Numerical examples are carried out to verify the theoretical results.
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页码:207 / 225
页数:19
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