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Superconvergence for multistep collocation

Authors: Ivar Lie and Syvert P. Nørsett
Journal: Math. Comp. 52 (1989), 65-79
MSC: Primary 65L05
MathSciNet review: 971403
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Abstract: One-step collocation methods are known to be a subclass of implicit Runge-Kutta methods. Further, one-leg methods are special multistep one-point collocation methods. In this paper we extend both of these collocation ideas to multistep collocation methods with k previous meshpoints and m collocation points. By construction, the order is at least $ m + k - 1$. However, by choosing the collocation points in the right way, order $ 2m + k - 1$ is obtained as the maximum. There are $ \left( {\begin{array}{*{20}{c}} {m + k - 1} \\ {k - 1} \\ \end{array} } \right)$ sets of such "multistep Gaussian" collocation points.

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Article copyright: © Copyright 1989 American Mathematical Society

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