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An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters

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Abstract

The manuscript contemplates a computationally robust numerical algorithm for the solution of a singularly perturbed 2D time-delayed parabolic convection-diffusion–reaction problem involving two small parameters. The operator-splitting algorithm on a uniform mesh is used in the time direction. To handle the abrupt change in the solution due to the presence of perturbation parameters, the upwind scheme is used in the spatial direction on a layer-rectifying mesh, namely, the Shishkin mesh. This makes the accuracy in space to be one (with a logarithmic term). The use of Bakhvalov-Shishkin mesh in the spatial domain rectifies this logarithmic effect on the rate of convergence. The highly efficient Thomas algorithm is used for the computation. The devised method is claimed to be parameter uniform and globally first-order accurate. All the theoretical claims are corroborated in practice with valid numerical tests.

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Data availability

The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The first author Ms. S. Priyadarshana conveys her profound gratitude to the DST, Govt. of India, for providing INSPIRE fellowship (IF 180938).

Funding

The first author would like to thank the Department of Science and Technology (DST), Govt. of India, for providing financial support to carry out her research work at NIT Rourkela.

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Author notes

  1. J. Mohapatra and S. Priyadarshana contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Rourkela, 769008, Odisha, India

    S. Priyadarshana & J. Mohapatra

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  1. S. Priyadarshana
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  2. J. Mohapatra
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Contributions

SP has done the analysis and computation and written the manuscript. JM has formulated the problem and done the formal analysis.

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Correspondence to J. Mohapatra.

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On behalf of the authors, Dr. Jugal Mohapatra shall be communicating the manuscript.

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Priyadarshana, S., Mohapatra, J. An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters. Numer Algor 97, 687–726 (2024). https://doi.org/10.1007/s11075-023-01720-9

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  • DOI: https://doi.org/10.1007/s11075-023-01720-9

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