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A robust numerical technique for weakly coupled system of parabolic singularly perturbed reaction–diffusion equations

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Abstract

This article presents a uniformly convergent numerical technique for a time-dependent reaction-dominated singularly perturbed system, including the same diffusion parameters multiplied with second-order spatial derivatives in all equations. Boundary layers are observed in the solution components for the small parameter. The proposed numerical technique consists of the Crank–Nicolson scheme in the temporal direction over a uniform mesh and quadratic \(\mathbb {B}\)-splines collocation technique over an exponentially graded mesh in the spatial direction. We derived the robust error estimates to establish the optimal order of convergence. Numerical investigations confirm the theoretical determinations and the proposed method’s efficiency and accuracy.

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Acknowledgements

The authors are grateful to the unknown reviewers for their insightful observations leading to the improvement of the manuscript. The first author is thankful to UGC, New Delhi, India, for providing the senior research fellowship (award letter No. 1078/(CSIR-UGC NET JUNE 2019)).

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India

    Satpal Singh & Devendra Kumar

  2. Department of Applied Mathematics, University of Salamanca, 37008, Salamanca, Spain

    J. Vigo-Aguiar

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  1. Satpal Singh
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  2. Devendra Kumar
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  3. J. Vigo-Aguiar
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Correspondence to Devendra Kumar.

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Singh, S., Kumar, D. & Vigo-Aguiar, J. A robust numerical technique for weakly coupled system of parabolic singularly perturbed reaction–diffusion equations. J Math Chem 61, 1313–1350 (2023). https://doi.org/10.1007/s10910-023-01464-w

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  • DOI: https://doi.org/10.1007/s10910-023-01464-w

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