✦ LIBER ✦
Conserving first integrals under discretization with variable step size integration procedures
✍ Scribed by Johannes Schropp
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 206 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
✦ Synopsis
It is well known that the application of one-step or linear multistep methods to an ordinary di erential equation with ÿrst integrals will destroy the conserving quantities. With the use of stabilization techniques similar to Ascher, Chin, Reich (Numer. Math. 67 (1997) 131-149) we derive stabilized variants of our original problem. We show that variable step size one-step and linear multistep methods applied to the stabilized equation will reproduce that phase portrait correctly. In particular, this technique will conserve ÿrst integrals over an inÿnite time interval within the local error of the used method.