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

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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 hyper-singular operator. Convergence in a Sobolev space setting is proven and the spectral convergence of the method is exhibited by numerical examples. © 2014 Rocky Mountain Mathematics Consortium.

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APA

Kress, R. (2014). A collocation method for a hypersingular boundary integral equation via trigonometric differentiation. Journal of Integral Equations and Applications, 26(2), 197–213. https://doi.org/10.1216/JIE-2014-26-2-197

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