Berry, Matthew M.Healy, Liam M.See also the dissertation of Matt Berry at http://scholar.lib.vt.edu/theses/available/etd-04282004-071227/A variable-step double-integration multi-step integrator is derived using divided differences. The derivation is based upon the derivation of Shampine-Gordon, a single-integration method. Variable-step integrators are useful for propagating elliptical orbits, because larger steps can be taken near apogee. As a double-integration method, the integrator performs only one function evaluation per step, whereas Shampine-Gordon requires two evaluations per step, giving the integrator a significant speed advantage over Shampine-Gordon. Though several implementation issues remain, preliminary results show the integrator to be effective.en-USnumerical integrationsecond order differential equationvariable stepShampine-Gordonmulti-stepStormer-CowellArticle