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An Introduction to Common Numerical Integration Codes Used in Dynamical Astronomy

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Dynamics of Small Solar System Bodies and Exoplanets

Part of the book series: Lecture Notes in Physics ((LNP,volume 790))

Abstract

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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Acknowledgments

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

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Authors and Affiliations

  1. Institute of Astronomy, University of Vienna, Türkenschanzstr. 17, 1880, Vienna, Austria

    S. Eggl & R. Dvorak

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  1. S. Eggl
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  2. R. Dvorak
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Correspondence to S. Eggl .

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Editors and Affiliations

  1. Dépt. Astronomie Fondamental, Observatoire de Paris, avenue de l Observatoire 61, Paris, 75014, France

    Jean J. Souchay

  2. Astronomisches Institut, Universität Wien, Türkenschanzstr. 17, Wien, 1180, Austria

    Rudolf Dvorak

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Eggl, S., Dvorak, R. (2010). An Introduction to Common Numerical Integration Codes Used in Dynamical Astronomy. In: Souchay, J., Dvorak, R. (eds) Dynamics of Small Solar System Bodies and Exoplanets. Lecture Notes in Physics, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04458-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-04458-8_9

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  • Online ISBN: 978-3-642-04458-8

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