Tanya Taidakova
CrAO
The most serious error of numerical simulations is the accumulation of discretization error due to a finite stepsize. The traditional integrators such as Runge-Kutta methods and multistep methods cause linear secular errors to the energy etc, which means that the semi-major axis and another orbital elements change linearly with time.
Potter [1] described the implicit second-order numerical method for particles in a plasma with magnetic field. We modificate this method and use for dynamics of particles around planet (or star) in the corotating coordinate system [2,3]. A big advantage of this numerical method is its absolute stability: the error depends only on the step size and does not accumulate with increasing number of time steps. In addition, this scheme takes less computing time (by a factor of approximately 1.5-2) than the second-order Runge-Kutta method. We tested this method for few astronomical system [2] and for motion of a asteroid in 1:1 Jupiter' resonance during 200 millions time steps [3].