Asymptotic bounds on the errors of one-step methods
In this note we show how to construct bounds using any one-step method endowed with an asymptotically correct local error estimator. The extrapolation codes vary their order from step to step. Correspondingly, we allow the one-step method to be changed at every step. The task breaks into three parts. In the next section we show how to construct asymptotic bounds on the local error. The following section outlines a global convergence proof which accounts for variation of formula from step to step and for the fact that the construction itself employs one of two formulas at each step. Finally the full construction and its justification are given. In a last section it is emphasized that asymptotic bounds may not be useful for assessing the general size of the global errors.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 6553534
- Report Number(s):
- SAND-83-0056; ON: DE83006924
- Country of Publication:
- United States
- Language:
- English
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