City Research Online

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 improve a FFT-based method for the Wiener-Hopf equation due to Henery by expressing it in terms of the Hilbert transform and computing the latter in a more sophisticated way with a sinc function expansion. We further enhance the error convergence using a spectral filter. We then generalise our method to the Fredholm equation by reformulating it as two coupled Wiener-Hopf equations and solving them iteratively. We provide numerical tests and open-source code.

Publication Type:	Article
Additional Information:	This is an open access article distributed under the terms of the Creative Commons CC BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Publisher Keywords:	Wiener-Hopf, Fredholm, integral equation, fast Fourier transform, fast Hilbert transform
Subjects:	Q Science > QA Mathematics
Departments:	Bayes Business School Bayes Business School > Faculty of Finance
SWORD Depositor:	Symplectic Administrator

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