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Oversampling collocation method for the Volterra integral equation with contaminated data

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Abstract

In this paper, an oversampling collocation method based on shifted generalized Jacobi functions as a set of basis is proposed to find the numerical solutions of Volterra integral equations with contaminated data. We proved that the oversampling collocation method decreases the covariance matrix of the coefficients vector of the approximated solution in the sense of 2-norm, which indicates the oversampling collocation method is more robust(which means anti-jamming of white noise) than the standard collocation method when the right side of the Volterra equation has contaminated data. Numerical experiments demonstrate the effectiveness of this method and its consistency with the theoretical analysis.

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Acknowledgements

The authors are very grateful to the reviewers for their comments and suggestions which have improved the paper. This work was supported partially by the Open Fund for the Sichuan National Applied Mathematics Center (no. 2022-KFJJ-01-002).

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Authors and Affiliations

  1. School of Sciences, Southwest Petroleum University, Chengdu, 610500, China

    Dazhi Zhao, Liang Pu & Yan Yu

  2. Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu, 610500, China

    Dazhi Zhao

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  1. Dazhi Zhao
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  2. Liang Pu
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  3. Yan Yu
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Correspondence to Dazhi Zhao.

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Zhao, D., Pu, L. & Yu, Y. Oversampling collocation method for the Volterra integral equation with contaminated data. Calcolo 59, 29 (2022). https://doi.org/10.1007/s10092-022-00473-6

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