The convergence of Nyström methods for Wiener-Hopf equations

G. A. Chandlen; I. G. Graham

doi:10.1007/BF01398884

The convergence of Nyström methods for Wiener-Hopf equations

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	345-364
Number of pages	20
Journal	Numerische Mathematik
Volume	52
Issue number	3
DOIs	https://doi.org/10.1007/BF01398884
Publication status	Published - May 1987

Keywords

Subject Classifications: AMS(MOS): 65R20, 45L10, CR: 5.18

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/BF01398884

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abstract = "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 Nystr{\"o}m 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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AB - 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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The convergence of Nyström methods for Wiener-Hopf equations

Abstract

Keywords

ASJC Scopus subject areas

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