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Discrete projection methods for Fredholm–Hammerstein integral equations using Kumar and Sloan technique

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Abstract

The proposed work discusses discrete collocation and discrete Galerkin methods for second kind Fredholm–Hammerstein integral equations on half line \([0,\infty )\) using Kumar and Sloan technique. In addition, the finite section approximation method is applied to transform the domain of integration from \([0, \infty )\) to \([0,\alpha ],~ \alpha >0\). In contrast to previous studies in which the optimal order of convergence is achieved for projection methods, we attained superconvergence rates in uniform norm using piecewise polynomial basis function. Moreover, these superconvergence rates are further enhanced by using discrete multi-projection (collocation and Galerkin) methods. In order to support the provided theoretical framework, numerical examples are included as well.

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Acknowledgements

We express our gratitude to the anonymous reviewers for their insightful and constructive comments which increased the quality of the paper.

Funding

The research of Dr. Gnaneshwar Nelakanti has been supported by the Science and Engineering Research Board (SERB) of India under the scheme “Mathematical Research Impact Centric Support (MATRICS), MTR/2021/000171.”

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Ritu Nigam & Gnaneshwar Nelakanti

  2. Department of Mathematics, Maharaja Manindra Chandra College, Kolkata, 700003, India

    Nilofar Nahid

  3. Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata, 741249, India

    Samiran Chakraborty

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  1. Ritu Nigam
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  2. Nilofar Nahid
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  3. Samiran Chakraborty
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  4. Gnaneshwar Nelakanti
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Correspondence to Ritu Nigam.

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Nigam, R., Nahid, N., Chakraborty, S. et al. Discrete projection methods for Fredholm–Hammerstein integral equations using Kumar and Sloan technique. Calcolo 61, 21 (2024). https://doi.org/10.1007/s10092-024-00573-5

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  • DOI: https://doi.org/10.1007/s10092-024-00573-5

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