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Paper: A New Stable Method for Long-Time Integration in an N-Body Problem
Volume: 125, Astronomical Data Analysis Software and Systems VI
Page: 174
Authors: Taidakova, Tanya
Abstract: The most serious error in numerical simulations is the accumulation of discretization error due to the finite stepsize. Traditional integrators such as Runge-Kutta methods cause linear secular errors to the energy, the semi-major axis, and the eccentricity of orbiting objects. Potter (1973) described an implicit second-order integrator for particles in a plasma with a magnetic field. We have used this integrator for an investigation of the dynamics of particles around a planet (or star) in a co-rotating coordinate system. A big advantage of this numerical integrator is its stability: the error in the semi-major axis and the eccentricity depends only on the step size and does not grow with an increasing number of time steps. The argument of pericenter changes linearly with time and more slowly than in the case of the Runge-Kutta integrator. In addition, this implicit integrator takes much less computing time than the second-order Runge-Kutta method. We tested this method for several astronomical systems and for motion of an asteroid in a 1:1 Jupiter resonance during 200 million time steps (about 5 million years or 800 thousand periods of asteroid resonance motion).
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