Engineering Computations ( IF 1.6 ) Pub Date : 2021-01-20 , DOI: 10.1108/ec-07-2020-0369 Subal Ranjan Sahu , Jugal Mohapatra
Purpose
The purpose of this study is to provide a robust numerical method for a two parameter singularly perturbed delay parabolic initial boundary value problem (IBVP).
Design/methodology/approach
To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. Here, the authors have used Shishkin type meshes for spatial discretization.
Findings
It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm.
Originality/value
This paper deals with the numerical study of a two parameter singularly perturbed delay parabolic IBVP. To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. The convergence analysis is carried out. It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm. Numerical experiments illustrate the efficiency of the proposed scheme.
中文翻译:
包含两个小参数的时滞抛物线微分方程的数值研究
目的
本研究的目的是为两参数奇异摄动延迟抛物线初始边界值问题 (IBVP) 提供一种稳健的数值方法。
设计/方法/方法
为了解决这个问题,作者使用了一种混合方案,结合了中点方案、迎风方案和二阶中心差分方案的空间导数。均匀网格上的后向 Euler 格式用于近似时间导数。在这里,作者使用 Shishkin 类型的网格进行空间离散化。
发现
观察到,所提出的方法关于离散最大范数以几乎二阶空间精度均匀收敛。
原创性/价值
本文涉及两个参数奇异摄动延迟抛物线 IBVP 的数值研究。为了解决这个问题,作者使用了一种混合方案,结合了中点方案、迎风方案和二阶中心差分方案的空间导数。均匀网格上的后向 Euler 格式用于近似时间导数。进行收敛分析。观察到,所提出的方法关于离散最大范数以几乎二阶空间精度均匀收敛。数值实验说明了所提出方案的效率。