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arXiv · 2106.05326

Solution of Wiener-Hopf and Fredholm integral equations by fast Hilbert and Fourier transforms

Guido Germano·Carolyn E Phelan·Daniele Marazzina·Gianluca Fusai
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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.

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Guido Germano, Carolyn E Phelan, Daniele Marazzina, Gianluca Fusai. 2021-06-09. Solution of Wiener-Hopf and Fredholm integral equations by fast Hilbert and Fourier transforms. https://arxiv.org/abs/2106.05326

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