A Spline Product Quasi-interpolation Method for Weakly Singular Fredholm Integral Equations

Authors:
Eero Vainikko;Gennadi Vainikko
Affiliations:
eero.vainikko@ut.ee;gennadi.vainikko@ut.ee
Venue:
SIAM Journal on Numerical Analysis
Year:
2008

Citing 0
Cited 4

Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind

Journal of Computational and Applied Mathematics
Nyström type methods for Fredholm integral equations with weak singularities

Journal of Computational and Applied Mathematics
B-spline quasi-interpolation on sparse grids

Journal of Complexity
Original article: Product quasi-interpolation method for weakly singular integral equation eigenvalue problem

Mathematics and Computers in Simulation

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Abstract

A discrete method of accuracy $O(h^{m})$ is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have weak diagonal and boundary singularities. The method is based on (i) improving the boundary behavior of the kernel with the help of a change of variables, and (ii) the product integration using quasi-interpolation by smooth splines of order $m$.