Efficient numerical method for highly oscillatory ordinary differential equations
Technical Report
·
OSTI ID:6424846
A quasi-envelope of the solution of highly oscillatory differential equations is defined. For many problems this is a smooth function which can be integrated by use of much larger steps than are possible for the original problem. Since the definition of the quasi-envelope is a differential equation involving an integral of the original oscillatory problem, it is necessary to integrate the original problem over a cycle of the oscillation (to average the effects of a full cycle). This information can then be extrapolated over a long (giant) time step. Unless the period is known a priori, it is also necessary to estimate it, either early in the integration (if it is fixed) or periodically (if it is slowly varying). Error propagation properties of this technique are investigated, and an automatic program is presented. Numberical results indicate that this technique is much more efficient than conventional ODE methods for many oscilating problems. 1 figure, 10 tables.
- Research Organization:
- Sandia Labs., Livermore, CA (USA)
- DOE Contract Number:
- EY-76-C-04-0789
- OSTI ID:
- 6424846
- Report Number(s):
- SAND-79-8204
- Country of Publication:
- United States
- Language:
- English
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