Statistics – Computation
Scientific paper
Nov 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002acasn..43..391w&link_type=abstract
Acta Astronomica Sinica, vol.43, no.4, p. 391-402
Statistics
Computation
5
Celestial Mechanics: Numerical Integration, Symplectic Integrators
Scientific paper
In 1996, Wisdom et al proposed the concept of corrector for a symplectic integrator and put it into practice. This is an intensive discussion with numerical comparison on symplectic correctors. Then it gives the method to derive the first and second correctors of any symplectic integrators by Lie series in a general case, in which the Hamiltonian can be separated into a main integrable part and several smaller integrable parts. Numerical experiments have been taken in a Sun-Jupiter-Saturn 3-body problem. It has shown that the first order corrector can raise precision, improve numerical stability, and has a good computer efficiency. Therefore, it deserves to be recommended. A large step size is usually adopted in the application of symplectic integrators. In this case the second order corrector has no notable advantages in raising precision. Furthermore, they would take much more computational time and should not be recommended.
Huang Tone-Yau
Wan Xiao-Sheng
Wu Xiaolin
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