Brunner, Hermann Iterated collocation methods and their discretizations for Volterra integral equations. (English) Zbl 0575.65134 SIAM J. Numer. Anal. 21, 1132-1145 (1984). Solving the inhomogeneous Fredholm integral equation of the second kind with smooth kernel numerically, it is known that iterated collocation approximation based on Gauss-Legendre knots produces superconvergence not only in the knots but over the complete interval of integration. The numerical integration procedure involved is Gaussian, using the collocation points as knots. In the present paper, the author shows that in the case of Volterra integral equations of the second kind superconvergence is also achieved by iterated collocation approximation using Gauss-Legendre knots in each subinterval, but only locally in the knots themselves. Numerical results for a specific example of a discrete iterated collocation method are given which confirm the predicted results on order convergence. Reviewer: G.Hämmerlin Cited in 1 ReviewCited in 44 Documents MSC: 65R20 Numerical methods for integral equations 45D05 Volterra integral equations Keywords:second kind; superconvergence; iterated collocation; Gauss-Legendre knots; Numerical results PDFBibTeX XMLCite \textit{H. Brunner}, SIAM J. Numer. Anal. 21, 1132--1145 (1984; Zbl 0575.65134) Full Text: DOI