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.

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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 -