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Weighted variable based numerical scheme for time-lagged semilinear parabolic problems including small parameter

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Abstract

A higher-order robust numerical algorithm is proposed for singularly perturbed semilinear parabolic partial differential equations having time lag. After dealing the semilinearity with Newton’s linearization technique, the time derivative is handled with the Crank–Nicolson scheme on a uniform mesh. The spatial derivatives are approached with a monotone hybrid finite difference scheme comprising the central difference scheme and the mid-point upwind scheme with variable weights on a layer-resolving mesh namely, the Shishkin mesh that provides a second-order accurate result upto a logarithmic factor. To overcome the obstacle of order reduction, the entire scheme is again solved on the Bakhvalov–Shishkin mesh. Thomas algorithm is used for computation. The proposed scheme is proved to be advantageous over some existing schemes in the literature.

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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 Department of Science and Technology, Govt. of India for providing INSPIRE fellowship (IF 180938).

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

    S. Priyadarshana & J. Mohapatra

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Priyadarshana, S., Mohapatra, J. Weighted variable based numerical scheme for time-lagged semilinear parabolic problems including small parameter. J. Appl. Math. Comput. 69, 2439–2463 (2023). https://doi.org/10.1007/s12190-023-01841-3

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