Abstract
We discuss superconvergence aspects of collocation methods for Volterra integral equations of the first kind. If piecewise polynomials of degree ≤ p are used, then convergence of order p + 2 is best possible. We show here that one may perform some postprocessing on the collocation solution to obtain convergence of order p + 3. This possibility arises because of the oscillating error in the collocation solution. The relevance of superconvergence techniques to a third order Runge-Kutta method is also discussed.
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© 1985 Birkhäuser Verlag Basel
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Eggermont, P.P.B. (1985). Beyond Superconvergence of Collocation Methods for Volterra Integral Equations of the First Kind. In: Hämmerlin, G., Hoffmann, KH. (eds) Constructive Methods for the Practical Treatment of Integral Equations. International Series of Numerical Mathematics, vol 73. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9317-6_9
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DOI: https://doi.org/10.1007/978-3-0348-9317-6_9
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9993-2
Online ISBN: 978-3-0348-9317-6
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