caa a22 4500 465821049 CHVBK 20180323112136.0 cr unu---uuuuu 170327e19900301xx s 000 0 eng 10.1007/BF01932138 doi (NATIONALLICENCE)springer-10.1007/BF01932138 Lie Ivar NDRE, Div. for Electronics, P.O. Box 25, N-2007, Kjeller, Norway aut Local error estimation for multistep collocation methods [Elektronische Daten] [Ivar Lie] Multistep collocation methods for initial value problems in ordinary differential equations are known to be a subclass of multistep Runge-Kutta methods and a generalisation of the well-known class of one-step collocation methods as well as of the one-leg methods of Dahlquist. In this paper we derive an error estimation method of embedded type for multistep collocation methods based on perturbed multistep collocation methods. This parallels and generalizes the results for one-step collocation methods by Nørsett and Wanner. Simple numerical experiments show that this error estimator agrees well with a theoretical error estimate which is a generalisation of an error estimate first derived by Dahlquist for one-leg methods. BIT Foundations, 1990 AMS(MOS): 65L05 nationallicence CR: 5.17 nationallicence Ordinary differential equations nationallicence initial value problems nationallicence numerical methods nationallicence error estimation nationallicence BIT Numerical Mathematics Kluwer Academic Publishers 30/1(1990-03-01), 126-144 0006-3835 30:1<126 1990 30 10543 https://doi.org/10.1007/BF01932138 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01932138 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lie Ivar NDRE, Div. for Electronics, P.O. Box 25, N-2007, Kjeller, Norway aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Kluwer Academic Publishers 30/1(1990-03-01), 126-144 0006-3835 30:1<126 1990 30 10543 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer