Germano, Guido;
Phelan, Carolyn E;
Marazzina, Daniele;
Fusai, Gianluca;
(2021)
Solution of Wiener-Hopf and Fredholm integral equations by fast Hilbert and Fourier transforms.
ArXiv: Ithaca, NY, USA.
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Abstract
We present numerical methods based on the fast Fourier transform (FFT) to solve convolution integral equations on a semi-infinite interval (Wiener-Hopf equation) or on a finite interval (Fredholm equation). We extend and improve a FFT-based method for the Wiener-Hopf equation due to Henery, expressing it in terms of the Hilbert transform, and computing the latter in a more sophisticated way with sinc functions. We then generalise our method to the Fredholm equation reformulating it as two coupled Wiener-Hopf equations and solving them iteratively. We provide numerical tests and open-source code.
| Type: | Working / discussion paper |
|---|---|
| Title: | Solution of Wiener-Hopf and Fredholm integral equations by fast Hilbert and Fourier transforms |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.48550/arXiv.2106.05326 |
| Publisher version: | https://doi.org/10.48550/arXiv.2106.05326 |
| Language: | English |
| Additional information: | This is an Open Access paper published under a Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). |
| Keywords: | math.NA, math.NA, cs.NA, 45B05, 65R20, 65T99 (Primary) 45E10, 44A15 (Secondary), G.1.9 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10190367 |
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