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Numerical difficulties with the gravitational n-body problem

Part of the Lecture Notes in Mathematics book series (LNM,volume 362)

Abstract

The gravitational n-body problem is unusually difficult to integrate reliably. In this review, the motion of a set of mass points under their forces of self-gravitation is asserted to be unstable in the sense of a hydrodynamical flow. While this does not imply that an n-body stellar system must collapse or explode, it does mean that we are attempting to treat an unstable system of differential equations by numerical methods. Many of the proofs of convergence or of numerical stability of integration methods are not applicable because they presuppose stability of the differential equations. The history of the problem is reviewed, experimental evidence is given in support of the assertion of instability, and a plea is made for arguments to justify inferences based on numerical experiments even though the differential equations may be unstable.

Keywords

  • Hard Sphere
  • Body Problem
  • Star Cluster
  • Stellar System
  • Phase Point

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1974 Springer-Verlag

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Miller, R.H. (1974). Numerical difficulties with the gravitational n-body problem. In: Bettis, D.G. (eds) Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations. Lecture Notes in Mathematics, vol 362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066595

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  • DOI: https://doi.org/10.1007/BFb0066595

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06602-6

  • Online ISBN: 978-3-540-37911-9

  • eBook Packages: Springer Book Archive