Abstract
Nyström's interpolation formula is applied to the numerical solution of singular integral equations. For the Gauss-Chebyshev method, it is shown that this approximation converges uniformly, provided that the kernel and the input functions possess a continuous derivative. Moreover, the error of the Nyström interpolant is bounded from above by the Gaussian quadrature errors and thus convergence is fast, especially for smooth functions. ForC ∞ input functions, a sharp upper bound for the error is obtained. Finally numerical examples are considered. It is found that the actual computational error agrees well with the theoretical derived bounds.
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This research has been partially supported by a grant from the Rutgers Research Council.
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Gerasoulis, A. Singular integral equations — The convergence of the Nyström interpolant of the Gauss-Chebyshev method. BIT 22, 200–210 (1982). https://doi.org/10.1007/BF01944477
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DOI: https://doi.org/10.1007/BF01944477