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[13.03] The Case for Explicit Runge-Kutta Nyström Methods

P.W. Sharp (University of Auckland)

Numerical analysts have long proposed high-order explicit Runge-Kutta Nyström (ERKN) methods as efficient non-symplectic methods for accurate N-body Newtonian simulations. Computational astronomers have largely ignored these methods, much preferring high-order Störmer methods. At first glance, Störmer methods are the obvious choice as they require just one evaluation of the acceleration per step as against up to 17 evaluations for existing high-order ERKN methods.

Motivated by recent developments with high-order ERKN methods, we re-examine the Störmer vs ERKN choice for simulations of the outer Solar System. We find the ERKN methods have favourable stability properties, smaller overhead and are a lot more competitive than a simple comparison using the number of evaluations per step would suggest.

This work was partly supported by the University of Auckland Research Committee and the Royal Society of New Zealand.

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Bulletin of the American Astronomical Society, 37 #2
© 2005. The American Astronomical Soceity.