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A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems

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Abstract

In this work, we propose a hybrid difference scheme for solving parameterized singularly perturbed delay differential problems. A unified error analysis framework for the proposed hybrid scheme is given that allows to conclude uniform convergence of \(\mathcal {O}(N^{-2}\ln ^{2} N)\) on Shishkin meshes and \(\mathcal {O}(N^{-2})\) on Bakhvalov meshes, where N is the number of mesh intervals in the domain. Numerical results are included to confirm the theoretical estimates.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Sunil Kumar

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

    Mukesh Kumar

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  1. Sunil Kumar
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  2. Mukesh Kumar
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Correspondence to Mukesh Kumar.

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Kumar, S., Kumar, M. A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems. Numer Algor 76, 349–360 (2017). https://doi.org/10.1007/s11075-016-0258-9

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  • DOI: https://doi.org/10.1007/s11075-016-0258-9

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