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A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem

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Abstract

In this article, we consider a class of singularly perturbed two-parameter parabolic partial differential equations with time delay on a rectangular domain. The solution bounds are derived by asymptotic analysis of the problem. We construct a numerical method using a hybrid monotone finite difference scheme on a rectangular mesh which is a product of uniform mesh in time and a layer-adapted Shishkin mesh in space. The error analysis is given for the proposed numerical method using truncation error and barrier function approach, and it is shown to be almost second- and first-order convergent in space and time variables, respectively, independent of both the perturbation parameters. At the end, we present some numerical results in support of the theory.

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Acknowledgements

The first author gratefully acknowledges the support of University Grant Commission, India, for research fellowship with reference no. 20/12/2015(ii)EU-V. The second author acknowledges the support of Science and Engineering Research Board (SERB) for the research grant with Project no. ECR/2017/000564. The authors gratefully acknowledge the valuable comments and suggestions from the anonymous referees.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi, Uttar Pradesh, India

    Sumit, Sunil Kumar &  Kuldeep

  2. Department of Mathematics, College of Charleston, Charleston, SC, 29424, USA

    Mukesh Kumar

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  1. Sumit
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  2. Sunil Kumar
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  3. Kuldeep
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  4. Mukesh Kumar
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Correspondence to Sunil Kumar.

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Communicated by José R Fernández.

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Sumit, Kumar, S., Kuldeep et al. A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem. Comp. Appl. Math. 39, 209 (2020). https://doi.org/10.1007/s40314-020-01236-1

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  • DOI: https://doi.org/10.1007/s40314-020-01236-1

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