Superconvergence for multistep collocation

Authors:
Ivar Lie and Syvert P. Nørsett

Journal:
Math. Comp. **52** (1989), 65-79

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1989-0971403-5

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 . However, by choosing the collocation points in the right way, order is obtained as the maximum. There are sets of such "multistep Gaussian" collocation points.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0971403-5

Article copyright:
© Copyright 1989
American Mathematical Society