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A priori and a posteriori error estimation for singularly perturbed delay integro-differential equations

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Abstract

This article deals with the numerical analysis of a class of singularly perturbed delay Volterra integro-differential equations exhibiting multiple boundary layers. The discretization of the considered problem is done using an implicit difference scheme for the differential term and a composite numerical integration rule for the integral term. The analysis of the discrete scheme consists of two parts. First, we establish an a priori error estimate that is used to prove robust convergence of the discrete scheme on Shishkin and Bakhvalov type meshes. Next, we establish the maximum norm a posteriori error estimate that involves difference derivatives of the approximate solution. The derived a posteriori error estimate gives the computable and guaranteed upper bound on the error. Numerical experiments confirm the theory.

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Acknowledgements

The authors would like to express great appreciation to anonymous reviewers and editor for their valuable comments and suggestions, which have helped to improve the quality and presentation of this paper.

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

    Sunil Kumar, Shashikant Kumar &  Sumit

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  1. Sunil Kumar
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  2. Shashikant Kumar
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Correspondence to Sunil Kumar.

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Kumar, S., Kumar, S. & Sumit A priori and a posteriori error estimation for singularly perturbed delay integro-differential equations. Numer Algor 95, 1561–1582 (2024). https://doi.org/10.1007/s11075-023-01620-y

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