Operational quadrature methods for Wiener-Hopf integral equations

Eggermont, P. P. B.; Lubich, Ch.

doi:10.1090/S0025-5718-1993-1160274-3

Operational quadrature methods for Wiener-Hopf integral equations
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by P. P. B. Eggermont and Ch. Lubich PDF

Math. Comp. 60 (1993), 699-718 Request permission

Abstract:

We study the numerical solution of Wiener-Hopf integral equations by a class of quadrature methods which lead to discrete Wiener-Hopf equations, with quadrature weights constructed from the Fourier transform of the kernel (or rather, from the Laplace transforms of the kernel halves). As the analytical theory of Wiener-Hopf equations is likewise based on the Fourier transform of the kernel, this approach enables us to obtain results on solvability and stability and error estimates for the discretization. The discrete Wiener-Hopf equations are solved by using an approximate Wiener-Hopf factorization obtained with FFT. Numerical experiments with the Milne equation of radiative transfer are included.

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