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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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
Keywords
- Fredholm–Hammerstein integral equations
- Superconvergence results
- Discrete projection methods with Kumar and Sloan technique
- Discrete multi-projection methods with Kumar and Sloan technique
- Piecewise polynomials