Spline collocation method for integro-differential equations with weakly singular kernels
Journal of Computational and Applied Mathematics
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Applied Numerical Mathematics
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Journal of Computational and Applied Mathematics
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Journal of Computational and Applied Mathematics
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Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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Journal of Computational and Applied Mathematics
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In the first part of this paper we study the regularity properties of solutions of linear Volterra integro-differential equations with weakly singular or other nonsmooth kernels. We then use these results in the analysis of two piecewise polynomial collocation methods for solving such equations numerically. The main purpose of the paper is the derivation of optimal global convergence estimates and the analysis of the attainable order of local superconvergence at the collocation points.