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2017 Central part interpolation schemes for integral equations with singularities
Kerli Orav-Puurand, Arvet Pedas, Gennadi Vainikko
J. Integral Equations Applications 29(3): 401-440 (2017). DOI: 10.1216/JIE-2017-29-3-401

Abstract

Two high order methods are constructed and analyzed for a class of Fredholm integral equations of the second kind with kernels that may have weak boundary and diagonal singularities. The proposed methods are based on improving the boundary behavior of the exact solution with the help of a change of variables, and on central part interpolation by polynomial splines on the uniform grid. A detailed error analysis for the proposed numerical schemes is given. This includes, in particular, error bounds under various types of assumptions on the equation, and shows that the proposed central part collocation approach has accuracy and numerical stability advantages compared with standard piecewise polynomial collocation methods, including the collocation at Chebyshev knots.

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Kerli Orav-Puurand. Arvet Pedas. Gennadi Vainikko. "Central part interpolation schemes for integral equations with singularities." J. Integral Equations Applications 29 (3) 401 - 440, 2017. https://doi.org/10.1216/JIE-2017-29-3-401

Information

Published: 2017
First available in Project Euclid: 14 August 2017

zbMATH: 1376.65158
MathSciNet: MR3695360
Digital Object Identifier: 10.1216/JIE-2017-29-3-401

Subjects:
Primary: 65R20

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.29 • No. 3 • 2017
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