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

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 $m$.

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