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A variable order method for the numerical integration of the gravitational N-body problem

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

Abstract

In an efficient computer program for numerical experiments with gravitational N-Body systems, at least one of the two following techniques is used: (1) regularization of the two-body close encounters, (2) variable and individual step size for each particle. Technique (1) involves frequent changes of the equations of motion and suggests the use of a one-step method. Technique (2) implies the solutions to be interpolated and extrapolated on non-step points and suggests the use of a power-series method.

A new tentative technique (2) is proposed, where the inconveniences associated with the individual step size scheme are avoided: the step size is the same for all the particles but the order of integration is variable and individual. A first application of this technique to a N-Body computer program with regularization of close encounters is developed.

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References

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© 1974 Springer-Verlag

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Janin, G. (1974). A variable order method for the numerical integration of 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/BFb0066597

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  • DOI: https://doi.org/10.1007/BFb0066597

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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