Aerospace Engineering Research Works

Permanent URI for this collectionhttp://hdl.handle.net/1903/1655

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Author: search.filters.author.Berry, Matthew M.Subject: search.filters.subject.second order differential equation

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    Speed and Accuracy Tests of the Variable-Step Störmer-Cowell Integrator
    (Univelt, Inc., 2005-02) Berry, Matthew M.; Healy, Liam M.
    The variable-step Stormer-Cowell integrator is a non-summed, double-integration multi-step integrator derived in variable-step form. The method has been implemented with a Shampine-Gordon style error control algorithm that uses an approximation of the local error at each step to choose the step size for the subsequent step. In this paper, the variable-step Stormer-Cowell method is compared to several other multi-step integrators, including the fixed-step Gauss-Jackson method, the Gauss-Jackson method with s-integration, and the variable-step single-integration Shampine- Gordon method, in both orbit propagation and orbit determination. The results show the variable-step Stormer-Cowell method is comparable with Gauss-Jackson using s-integration, except in high drag cases where the variable-step Stormer-Cowell method has an advantage in speed and accuracy.
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    A Variable-Step Double-Integration Multi-Step Integrator
    (Univelt, Inc., 2004-02) Berry, Matthew M.; Healy, Liam M.
    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.