TY - JOUR
T1 - An introduction to common numerical integration codes used in dynamical astronomy
AU - Eggl, S.
AU - Dvorak, R.
N1 - Funding Information:
S. Eggl would like to acknowledge the support from Austrian FWF Project P-20216. R. Dvorak would like to acknowledge the support from Austrian FWF Project P-18930 – N16
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77950274058&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77950274058&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-04458-8_9
DO - 10.1007/978-3-642-04458-8_9
M3 - Article
AN - SCOPUS:77950274058
SN - 0075-8450
VL - 790
SP - 431
EP - 480
JO - Lecture Notes in Physics
JF - Lecture Notes in Physics
ER -