Comparison of Accuracy Assessment Techniques for Numerical Integration

Knowledge of accuracy of numerical integration is important for composing an overall numerical error budget; in orbit determination and propagation for space surveillance, there is frequently a computation time-accuracy tradeoff that must be balanced. There are several techniques to assess the accuracy of a numerical integrator. In this paper we compare some of those techniques: comparison with two-body results, with step-size halving, with a higher-order integrator, using a reverse test, and with a nearby exactly integrable solution (Zadunaisky’s technique). Selection of different kinds of orbits for testing is important, and an RMS error ratio may be constructed to condense results into a compact form. Our results show that stepsize halving and higher-order testing give consistent results, that the reverse test does not, and that Zadunaisky’s technique performs well with a single-step integrator, but that more work is needed to implement it with a multi-step integrator.