A robust numerical method for a coupled system of singularly perturbed parabolic delay problems
ISSN: 0264-4401
Article publication date: 6 August 2020
Issue publication date: 8 February 2021
Abstract
Purpose
The purpose of this paper is to design and analyze a robust numerical method for a coupled system of singularly perturbed parabolic delay partial differential equations (PDEs).
Design/methodology/approach
Some a priori bounds on the regular and layer parts of the solution and their derivatives are derived. Based on these a priori bounds, appropriate layer adapted meshes of Shishkin and generalized Shishkin types are defined in the spatial direction. After that, the problem is discretized using an implicit Euler scheme on a uniform mesh in the time direction and the central difference scheme on layer adapted meshes of Shishkin and generalized Shishkin types in the spatial direction.
Findings
The method is proved to be robust convergent of almost second-order in space and first-order in time. Numerical results are presented to support the theoretical error bounds.
Originality/value
A coupled system of singularly perturbed parabolic delay PDEs is considered and some a priori bounds are derived. A numerical method is developed for the problem, where appropriate layer adapted Shishkin and generalized Shishkin meshes are considered. Error analysis of the method is given for both Shishkin and generalized Shishkin meshes.
Keywords
Acknowledgements
This research was supported by the Science and Engineering Research Board under the Project No. ECR/2017/000564. The second and fourth authors gratefully acknowledge the support of the Council of Scientific and Industrial Research, New Delhi, India, for research fellowship with Sanction No.: 09/1217(0017)/2015-EMR-I and 09/1217(0035)/2018-EMR-I, respectively.
Citation
Kumar, M., Singh, J., Kumar, S. and , A. (2021), "A robust numerical method for a coupled system of singularly perturbed parabolic delay problems", Engineering Computations, Vol. 38 No. 2, pp. 964-988. https://doi.org/10.1108/EC-04-2020-0191
Publisher
:Emerald Publishing Limited
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