Abstract
Round-off error accumulation in numerical integration of the equations of motion in an inverse square field has been studied for approximately circular orbits. The second order equations of motion in Cowell formulation were assumed to be integrated with a one-step method of arbitrary order after reduction to a first order system. Analytical expressions for the first two statistical moments of the accumulated error in one position component have been derived via the adjoint method for particular classes of fixed and floating point arithmetics. The error mean increases linearily or quadratically with time dependent on the mechanization of the ADD-instruction regardless of number system (sign-magnitude or two’s complement) and method of scaling (fixed or floating point). The error variance increases with third power of time.
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