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Superconvergence results for non-linear Hammerstein integral equations on unbounded domain

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Abstract

Many physical problems represented as initial and boundary value problems are usually solved by transforming them into integral equations on the half-line. Therefore, this paper discusses the Galerkin and collocation methods along with the multi-Galerkin and multi-collocation methods for non-linear integral equations with compact and Wiener-Hopf kernel operators on the half-line in the space of piecewise polynomial subspaces. As Hammerstein integral equation on half-line has the unbounded domain, the finite section approximation method is applied; and afterward, we find an approximate solution for the finite section integral equation. In order to obtain improved superconvergence rates, we apply Sunil Kumar’s method and then compare proposed convergence rates with the existing results of Nahid et al. [22] both theoretically and numerically. These results are further improved by applying multi-projection methods. In addition, it has shown that the proposed theory enhances the results of [22]. Finally, numerical examples are presented to demonstrate the given theoretical framework.

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Acknowledgements

The editors and anonymous reviewers have our sincere gratitude for their insightful comments, which significantly raised the paper’s quality.

Funding

The Science and Engineering Research Board (SERB) of India has funded Dr. Gnaneshwar Nelakanti’s research 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, 721302, India

    Ritu Nigam, Samiran Chakraborty & Gnaneshwar Nelakanti

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

    Nilofar Nahid

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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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Contributions

Conceptualization: Gnaneshwar Nelakanti, Ritu Nigam. Analysis: Ritu Nigam. Methodology: Ritu Nigam, Gnaneshwar Nelakanti. Supervision: Gnaneshwar Nelakanti, Nilofar Nahid, Samiran Chakraborty. Software: Nilofar Nahid. Writing–original draft: Ritu Nigam. Writing–review and editing: Ritu Nigam, Gnaneshwar Nelakanti, Samiran Chakraborty.

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Correspondence to Ritu Nigam.

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Nigam, R., Nahid, N., Chakraborty, S. et al. Superconvergence results for non-linear Hammerstein integral equations on unbounded domain. Numer Algor 94, 1243–1279 (2023). https://doi.org/10.1007/s11075-023-01534-9

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