Comparison Of Accuracy Assessment Techniques For Numerical Integration
in Scheeres, Pittelkau, Proulx, Cangahuala eds., Spaceflight Mechanics 2003, Vol. 114 in Advances in the Astronautical Sciences, pp. 1003-1016
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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 step- size 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.
See also dissertation of Matt Berry at http://scholar.lib.vt.edu/theses/available/etd-04282004-071227/