Global error estimation for stiff ODEs
Some years ago we devised a way to estimate the global error when solving stiff ODEs which is interesting because it is very simple and very cheap. Undoubtedly the most popular codes for the solution of stiff ODEs are based on the backward differentiation formulas (BDF). The scheme described in applied to the BDF of orders 1 to 3 but not to orders 4 to 6. Because we were unable to handle the popular codes which all vary the order of the BDF used between one and five, we gave the scheme only the limited circulation of a report. On returning to the matter recently we saw how to broaden the applicability of the method greatly, in particular to include all the BDF, and to understand much better an important approximation made. We explain this new treatment of our approach to global error estimation. Since the report, Prothero has given an approach to estimation of global error which is closely related to the way we now view our approach. We shall review his approach and contrast his assumptions with the ones we make and point out an important restriction. Finally we draw upon an approximation made by Prothero to extend the applicability of the procedure developed, in some cases to improve the accuracy of the procedure.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 6181341
- Report Number(s):
- SAND-82-2517C; CONF-830603-1; ON: DE83003294
- Country of Publication:
- United States
- Language:
- English
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