A fully discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on “central part” interpolation by polynomials on the uniform grid.
Orav-Puurand, K. (2013). A central part interpolation scheme for log-singular integral equations. Mathematical Modelling and Analysis, 18(1), 136-148. https://doi.org/10.3846/13926292.2013.760114
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