Fixed vs variable order Runge-Kutta
Technical Report
·
OSTI ID:6436000
Popular codes for the numerical solution of non-stiff ordinary differential equations (ODEs) are based on a (fixed order) Runge-Kutta method, a variable order Adams method, or an extrapolation method. Extrapolation can be viewed as a variable order Runge-Kutta method. It is plausible that variation of order could lead to a much more efficient Runge-Kutta code, but numerical comparisons have been contradictory. We reconcile previous comparisons by exposing differences in testing methodology and incompatibilities of the implementations tested. An experimental Runge-Kutta code is compared to a state-of-the-art extrapolation code. With some qualifications, the extrapolation code shows no advantage. Extrapolation does not appear to be a particularly effective way to vary the order of Runge-Kutta methods. Although a good way to solve non-stiff problems, our tests raise the question as to whether there is any point to pursuing it as a separate method. 30 references, 15 figures.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 6436000
- Report Number(s):
- SAND-84-1410; ON: DE85001320
- Country of Publication:
- United States
- Language:
- English
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