The piecewise polynomial collocation method is discussed to solve second kind Fredholm integral equations with weakly singular kernelsK(t, s) which may be discontinuous ats = 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.
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