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We present numerical methods based on the fast Fourier transform (FFT) tosolve convolution integral equations on a semi-infinite interval (Wiener-Hopfequation) or on a finite interval (Fredholm equation). We extend and improve aFFT-based method for the Wiener-Hopf equation due to Henery, expressing it interms of the Hilbert transform, and computing the latter in a moresophisticated way with sinc functions. We then generalise our method to theFredholm equation reformulating it as two coupled Wiener-Hopf equations andsolving them iteratively. We provide numerical tests and open-source code.

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