Electronic Resource
Springer
BIT
30 (1990), S. 126-144
ISSN:
1572-9125
Keywords:
AMS(MOS): 65L05
;
CR: 5.17
;
Ordinary differential equations
;
initial value problems
;
numerical methods
;
error estimation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01932138
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