A high order robust numerical scheme for singularly perturbed delay parabolic convection diffusion problems

被引：15
作者：
Babu, Gajendra [1 ]
Bansal, Komal [2 ]
机构：
[1] South Asian Univ, Dept Math, New Delhi, India
[2] Panjab Univ, Dev Samaj Coll Women, Chandigarh, India
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2022年 / 68卷 / 01期
关键词：
Non standard finite difference method; Richardson extrapolation; Time delay; Convection diffusion; Parabolic PDEs; Implicit Euler’ s scheme;
D O I：
10.1007/s12190-021-01512-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a robust non standard numerical scheme has been analysed for singularly perturbed parabolic convection-diffusion problems with time delay. The numerical scheme comprises of implicit Euler method, Richardson extrapolation technique and non standard techniques developed by Mickens. Parameter uniform estimates for stability and consistency have been proved. Numerical experiments have been carried out to corroborate the theoretical results.
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收藏
页码：363 / 389
页数：27
相关论文
共 22 条
[1]   A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations [J].
Ansari, A. R. ;
Bakr, S. A. ;
Shishkin, G. I. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 205 (01) :552-566
[2]   Parameter uniform numerical scheme for time dependent singularly perturbed convection-diffusion-reaction problems with general shift arguments [J].
Bansal, Komal ;
Sharma, Kapil K. .
NUMERICAL ALGORITHMS, 2017, 75 (01) :113-145
[3]   A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation [J].
Bashier, E. B. M. ;
Patidar, K. C. .
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (09) :4728-4739
[4]   A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems [J].
Clavero, C ;
Jorge, JC ;
Lisbona, F .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 154 (02) :415-429
[5]   Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection-diffusion problems on Shishkin mesh [J].
Das, Abhishek ;
Natesan, Srinivasan .
APPLIED MATHEMATICS AND COMPUTATION, 2015, 271 :168-186
[6]   A higher order difference method for singularly perturbed parabolic partial differential equations [J].
Das, Pratibhamoy .
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2018, 24 (03) :452-477
[7]  
Farrell P.A., 1991, P 13 IMACS WORLD C C, V91, P501
[8]  
Friedman A., 1964, Partial Differential Equations of Parabolic Type
[9]   ε-Uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations [J].
Gowrisankar, S. ;
Natesan, Srinivasan .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2017, 94 (05) :902-921
[10]  
Gowrisankar S, 2014, ELECTRON T NUMER ANA, V41, P376
123