Journal of Integral Equations and Applications

A collocation method for a hypersingular boundary integral equation via trigonometric differentiation

Rainer Kress

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Abstract

Revisiting the author's paper from 1995 on this topic, a fully discrete collocation method is proposed for the hypersingular integral equation arising from the double-layer approach for the solution of Neumann boundary value problems in two dimensions which is based on trigonometric differentiation to discretize the principal part of the hypersingular operator. Convergence in a Sobolev space setting is proven and the spectral convergence of the method is exhibited by numerical examples.

Article information

Source
J. Integral Equations Applications, Volume 26, Number 2 (2014), 197-213.

Dates
First available in Project Euclid: 21 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1405949662

Digital Object Identifier
doi:10.1216/JIE-2014-26-2-197

Mathematical Reviews number (MathSciNet)
MR3233518

Zentralblatt MATH identifier
1310.65169

Citation

Kress, Rainer. A collocation method for a hypersingular boundary integral equation via trigonometric differentiation. J. Integral Equations Applications 26 (2014), no. 2, 197--213. doi:10.1216/JIE-2014-26-2-197. https://projecteuclid.org/euclid.jiea/1405949662


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