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

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Abstract

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.

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Acknowledgements

The authors express their sincere thanks to the referees whose valuable comments helped to improve the presentation.

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  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781 039, India

    Maneesh Kumar Singh & Srinivasan Natesan

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  1. Maneesh Kumar Singh
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  2. Srinivasan Natesan
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Correspondence to Srinivasan Natesan.

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Singh, M.K., Natesan, S. Numerical Analysis of Singularly Perturbed System of Parabolic Convection–Diffusion Problem with Regular Boundary Layers. Differ Equ Dyn Syst 30, 695–717 (2022). https://doi.org/10.1007/s12591-019-00462-2

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