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We propose a piecewise polynomial collocation method for solving linear Volterra integral equations of the second kind with kernels which, in addition to a weak diagonal singularity, may have a weak boundary singularity. Global convergence estimates are derived and a collection of numerical results is given.doi:10.3846/1392-6292.2009.14.79-89 fatcat:jbbgfpj2c5euzfvz4jhwnejqcm