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01-06-2024

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

Authors: Ritu Nigam, Nilofar Nahid, Samiran Chakraborty, Gnaneshwar Nelakanti

Published in: Calcolo | Issue 2/2024

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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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Title: Discrete projection methods for Fredholm–Hammerstein integral equations using Kumar and Sloan technique
Authors: Ritu Nigam
Nilofar Nahid
Samiran Chakraborty
Gnaneshwar Nelakanti
Publication date: 01-06-2024
Publisher: Springer International Publishing
Published in: Calcolo / Issue 2/2024
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-024-00573-5

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

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