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A posteriori error estimation in maximum norm for a system of singularly perturbed Volterra integro-differential equations

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Abstract

In this paper, a system of singularly perturbed Volterra integro-differential equations is considered. The backward Euler formula is used to discretize the differential part and the right-hand rectangle rule is applied to approximate the integral term. The stabilities of the continuous and discrete solutions are carried out using the Grönwall’s inequality, respectively. The a posterior error bounds are given to design an adaptive grid generation algorithm. Numerical results complement the theoretical results.

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Acknowledgements

This work is supported by the National Science Foundation of China (11761015, 11826211), the Natural Science Foundation of Guangxi (2020GXNSFAA159010), the key project of Guangxi Natural Science Foundation (2017GXNSFDA198014, 2018GXNSFDA050014), Zhejiang Province Public Welfare Technology Application Research Project (LGF19A010001), and Ningbo Municipal Natural Science Foundation (2019A610045).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanning Normal University, Nanning, 530029, China

    Ying Liang & Li-Bin Liu

  2. Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, China

    Zhongdi Cen

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  1. Ying Liang
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  2. Li-Bin Liu
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  3. Zhongdi Cen
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Correspondence to Li-Bin Liu.

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Communicated by Hui Liang.

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Liang, Y., Liu, LB. & Cen, Z. A posteriori error estimation in maximum norm for a system of singularly perturbed Volterra integro-differential equations. Comp. Appl. Math. 39, 255 (2020). https://doi.org/10.1007/s40314-020-01303-7

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  • DOI: https://doi.org/10.1007/s40314-020-01303-7

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