Abstract
Abstract Approximations to a solution and its derivatives of a boundary value problem of an nth order linear Fredholm integro-differential equation with weakly sin-gular or other nonsmooth kernels have been determined. These approximations are piecewise polynomial functions on special graded grids. To find them, a fully discrete version of the Galerkin method has been constructed. This version is based on a dis-crete inner product concept and some suitable product integration techniques. Optimal global convergence estimates have been derived and a collection of numerical results of a test problem is given.
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