Numerical Analysis of Singularly Perturbed System of Parabolic Convection–Diffusion Problem with Regular Boundary Layers

被引：0
作者：
Maneesh Kumar Singh
Srinivasan Natesan
机构：
[1] Indian Institute of Technology Guwahati,Department of Mathematics
来源：
Differential Equations and Dynamical Systems | 2022年 / 30卷
关键词：
Singularly perturbed system; Parabolic convection–diffusion problems; Boundary layers; Shishkin mesh; Finite difference scheme; Uniform convergence; AMS 65M06; 65M12; CR G1.8;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this article, we obtain the numerical solution of singularly perturbed system of parabolic convection–diffusion problems exhibiting boundary layer. The proposed numerical scheme consists of the backward-Euler method for the time derivative and an upwind finite difference scheme for the spatial derivatives. We analyze the scheme on a piecewise-uniform Shishkin mesh for the spatial discretization to establish uniform convergence with respect to the perturbation parameters. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimate is derived. In order to validate the theoretical results, we have carried out some numerical experiments.
引用
收藏
页码：695 / 717
页数：22
相关论文
共 19 条
[1]  
Bellew S(2004)A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations Appl. Numer. Math. 51 171-186
[2]  
O’Riordan E(2005)Parameter-uniform finite difference scheme for a system of coupled singularly perturbed convection-diffusion equations Int. J. Comput. Math. 82 177-192
[3]  
Cen Z(2013)Numerical solution of a system of singularly perturbed convection-diffusion boundary-value problems using mesh equidistribution technique Aust. J. Math. Anal. Appl. 10 17-200
[4]  
Das P(2008)Richardson extrapolation mehtod for singularly perturbed coupled system of convection-diffusion boundary-value problems CMES Comput. Model. Eng. Sci. 38 179-1301
[5]  
Natesan S(2016)A novel technique for constructing difference schemes for systems of singularly perturbed equations Commun. Comput. Phys. 19 1287-32
[6]  
Deb BS(2007)Analysis of an upwind finite-difference scheme for a system of coupled singularly perturbed convection-diffusion equations. Computing 79 23-16
[7]  
Natesan S(2014)A robust adaptive grid method for a system of two singularly perturbed convection-diffusion equations with weak coupling J. Sci. Comput. 61 1-310
[8]  
Hsieh P-W(1988)Numerical methods for time-dependent convection-diffusion equations J. Comput. Appl. Math. 21 289-121
[9]  
Shih Y-T(2009)Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems Adv. Comput. Math. 30 101-undefined
[10]  
Yang S-Y(undefined)undefined undefined undefined undefined-undefined
12