Multistep Methods for Integrating the Solar System
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
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High order multistep methods, run at constant stepsize, are one of the most effective schemes for integrating the Newtonian solar system, for extended periods of time. The stability and error growth of these methods is studied when applied to harmonic oscillators and two body systems like the Sun- Jupiter pair. The truncation error of multistep methods on two-body systems grows in time like t-sq, and the roundoff like t to the 1.5th power, and a theory is given that accounts for this. A better design is attempted for multistep integrators than the traditional Stormer and Cowell methods, and a few interesting ones are found. A second result of this search for new methods is that no predictor were found that is stable on the Sun-Jupiter system, for stepsizes smaller than 108 steps per cycle whose order of accuracy is greater than 12. For example, Stormer-13 becomes unstable at 108 steps per cycle. This limitation between stability and accuracy seems to be a general property of multistep methods.
- Celestial Mechanics