The piecewise polynomial collocation method is discussed to solve second kind Fredholm integral equations with weakly singular kernels K (t, s) which may be discontinuous at s = d, d = const. The main result is given in Theorem 4.1. Using special collocation points, error estimates at the collocation points are derived showing a more rapid convergence than the global uniform convergence in the interval of integration available by piecewise polynomials.
Hakk, K., & Pedas, A. (1998). Numerical solutions and their superconvergence for weakly singular integral equations with discontinuous coefficients. Mathematical Modelling and Analysis, 3(1), 104-113. https://doi.org/10.3846/13926292.1998.9637093
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