Summary
We consider second kind integral equations on the half-line; where the integral operator is a compact perturbation of a convolution operator. It is shown that these may be solved numerically by Nyström methods based on composite quadrature rules. Provided the underlying mesh is graded to correctly match the behaviour of the solution, we prove the same rates of convergence that occur when the methods are applied to equations on finite intervals. Numerical examples are given.
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Supported by a visiting fellowship at the Centre for Mathematical Analysis, Australian National University, Canberra
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Chandlen, G.A., Graham, I.G. The convergence of Nyström methods for Wiener-Hopf equations. Numer. Math. 52, 345–364 (1987). https://doi.org/10.1007/BF01398884
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DOI: https://doi.org/10.1007/BF01398884