Summary
This paper deals with the question of the attainable order of convergence in the numerical solution of Volterra and Abel integral equations by collocation methods in certain piecewise polynomial spaces and which are based on suitable interpolatory quadrature for the resulting moment integrals. The use of a (nonlinear) variation of constants formula for the representation of the error function in terms of the defect allows for a unified treatment of equations with continuous and weakly singular kernels.
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Brunner, H., Nørsett, S.P. Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind. Numer. Math. 36, 347–358 (1981). https://doi.org/10.1007/BF01395951
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DOI: https://doi.org/10.1007/BF01395951