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Numerical Algorithms

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22.08.2023 | Original Paper

Jacobi spectral projection methods for Fredholm integral equations of the first kind

verfasst von: Subhashree Patel, Bijaya Laxmi Panigrahi

Erschienen in: Numerical Algorithms | Ausgabe 1/2024

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Abstract

In this paper, we employ Tikhonov regularization method with the projection methods using Jacobi polynomial bases to the first kind of Fredholm integral equations to find the approximate solution. We discuss the convergence analysis and obtain the convergence rates in \(\varvec{L}^{\textbf{2}}_{\varvec{w}^{\varvec{\alpha ,\beta }}}\) norm under a priori parameter choice strategy. We also consider the Engl-type discrepancy principle as a posteriori parameter strategy for finding the regularization parameter and also evaluate the convergence rate which is of optimal order. Finally, we provide the numerical experiments to justify the theoretical results.

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Titel: Jacobi spectral projection methods for Fredholm integral equations of the first kind
verfasst von: Subhashree Patel
Bijaya Laxmi Panigrahi
Publikationsdatum: 22.08.2023
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 1/2024
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-023-01638-2

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