Uniformly convergent numerical method for singularly perturbed two parameter time delay parabolic problem

被引：0
作者：
Govindarao L. [1 ]
Mohapatra J. [1 ]
Sahu S.R. [1 ]
机构：
[1] Department of Mathematics, National Institute of Technology, Rourkela
来源：
International Journal of Applied and Computational Mathematics | 2019年 / 5卷 / 3期
关键词：
Singular perturbation; Time delay; Two parameter problem; Uniform convergence; Upwind scheme;
D O I：
10.1007/s40819-019-0672-5
中图分类号：
学科分类号：
摘要：
This paper discusses the numerical solution of one dimensional parabolic convection– reaction–diffusion time delay problem with two small parameters. For the discretization of the time derivative, we use the implicit Euler scheme on a uniform mesh and for the spatial discretization, we use the upwind difference scheme on the Shishkin type meshes (standard Shishkin mesh, Bakhvalov–Shishkin mesh). We prove that numerically the proposed method is provides a first order convergence, which is optimal for this case. Finally, to support the theoretical results, we present some numerical experiments using the proposed method. © Springer Nature India Private Limited 2019.
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