Journal of Integral Equations and Applications

Central part interpolation schemes for integral equations with singularities

Kerli Orav-Puurand, Arvet Pedas, and Gennadi Vainikko

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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.

Article information

Source
J. Integral Equations Applications, Volume 29, Number 3 (2017), 401-440.

Dates
First available in Project Euclid: 14 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1502676096

Digital Object Identifier
doi:10.1216/JIE-2017-29-3-401

Mathematical Reviews number (MathSciNet)
MR3695360

Zentralblatt MATH identifier
1376.65158

Subjects
Primary: 65R20: Integral equations

Keywords
Central part interpolation integral equations with weakly singular kernels collocation method product integration method

Citation

Orav-Puurand, Kerli; Pedas, Arvet; Vainikko, Gennadi. Central part interpolation schemes for integral equations with singularities. J. Integral Equations Applications 29 (2017), no. 3, 401--440. doi:10.1216/JIE-2017-29-3-401. https://projecteuclid.org/euclid.jiea/1502676096


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