An introduction to common numerical integration codes used in dynamical astronomy

S. Eggl, R. Dvorak

Research output: Contribution to journalArticlepeer-review


As the tree of numerical methods used to solve ordinary differential equations develops more and more branches, it may, despite great literature, become hard to find out which properties should be aimed for, given certain problems in celestial mechanics. With this chapter the authors intend to give an introduction to common, symplectic, and non-symplectic algorithms used to numerically solve the basic Newtonian gravitational N-body problem in dynamical astronomy. Six methods are being presented, including a Cash-Karp Runge-Kutta, Radau15, Lie Series, Bulirsch-Stoer, Candy, and a symplectic Hybrid integrator of Mon. Not.R. Astro. Soc. 304: 793-799,?]. Their main properties, as for example, the handling of conserved quantities, will be discussed on the basis of the Kepler problem.

Original languageEnglish (US)
Pages (from-to)431-480
Number of pages50
JournalLecture Notes in Physics
StatePublished - 2010
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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