Numerical solutions and their superconvergence for weakly singular integral equations with discontinuous coefficients - Hakk, Kristiina; Pedas, Arvet (Mathematical Modelling and Analysis, 1998)
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.First Published Online: 14 Oct 2010